How many numbers in the sequence 16, 18, 20, 22, 24..... should be taken to get an average 100.

Surit Datta   9 years AGO

according to the AP series summation formula we know,
Sn = n/2*[2*a1 + (n - 1)*d]
where Sn is the summation of the series,
n is the number of terms,
a1 is the 1st term,
d is the difference between two successive number,
so in the above formula
if we put,
Sn as 100*n
a1 = 16
d = 2
so we get n as 85
so option 5
that's it.

Like? Yes (16) | No   

sourabh verma   9 years AGO

sum of n terms in ap is
s=n/2[2a+(n-1)*d]
so by this we will get sum
and average =sum/no. of terms
by solving both the equation
no of terms 85

Like? Yes (3) | No   

Santhoshkumar   9 years AGO

sum of n term /n=100;
n/2(2a+(n-1)d)/n=100;
n=85

Like? Yes (3) | No (1)  

NESAB JAFAR   9 years AGO

using arithmetic mean

Like? Yes (2) | No   

Supriya Mondal   9 years AGO

We know that,sum of first n terms of an A.P. series is
Sn = (n/2)[2a +(n -1)d]
Here, Sn=n*100
a=16
d=2
So, we can write,
(n/2)[2*16+(n-1)*2]=n*100
then, 32+2*n-2=200
then,2*n=170
then, n=85
So, option 5)85 is the right answer

Like? Yes (3) | No (1)  

shareef   9 years AGO

16,18,.... Upto n terms then
sum of n terms = (2a+(n-1)d)n/2
a=16, d= 2
we know sum / n = 100
2n = 170
n= 85

Like? Yes (2) | No   

Yathiraj   9 years AGO

16, 18, 20, 22.... 184 => 85 number
(sum of all) / 85 = 100

Option 5.

Actually, you can take only 2 number 16 & 184 where (16+184)/2 = 100. The problem statement doesn't say that you have to take numbers sequentially without skipping. :) But the option 2 is not in the list so, I have to go with option 5. :)

Like? Yes (3) | No (1)  

SHAHEEN   9 years AGO

n/2(30+2n)=100n
n=100-15
n=85--option 5 is ans

Like? Yes (2) | No   

susmit   9 years AGO

Sn = n/2 [2a + (n-1)d]

Therefore : {n/2 [2(16) + (n-1)2] } / n = 100
(since a= 16 & d=2)
= {n/2[32 + 2n -2] } / n =100

= {n/2 [ 30+2n ] } / n = 100

= 30 + 2n = 200

= 2n = 170
Therefore n =85. Hence 85 numbers should be taken.
Option no. (5)

Like? Yes (2) | No (1)  

SUSHANT KUMAR   9 years AGO

sequence 16, 18, 20, 22, 24.....has a gap of 2.
so to get average 100. last term should be 184.
i.e. (16+184)/2=100
so no of terms =85

Like? Yes (1) | No   

aman aditya   9 years AGO

43rd term of the series is 100
So there are 42 term before 100
So there must have 42'term after 100 to have 100"as average
Hence 42+1+42=85 term

Like? Yes (2) | No (1)  

GIRISH TYAGI   9 years AGO

n/2(2*16 + (n-1)2) = 100*n
n=85

Like? Yes (2) | No (1)  

Md Shahid Akhter   9 years AGO

Sum upto n numbers S= n/2{2a +(n-1)d}
Average of n numbers= S/n = 1/2{2*16+(n-1)2}= 15+n
Given,
Average = 100 =15+n
n=85

Like? Yes (2) | No (1)  

RAKESH   9 years AGO

100n = n/2 * [2*16 +(n-1)2]
=> n = 85

Like? Yes (1) | No   

sompon temtheerakij   9 years AGO

16+18+.....................+182+184
av = 100
(184-16)/2+1 = 85

Like? Yes (1) | No   

SANTOSH SAHOO   9 years AGO

this is an A.P sequence so..
here a=16
d=2

sum of n term=n/2[2*a+(n-1)d]
=>avrg=sum of n term/n

=>100=( n/2[2*a+(n-1)d] )/n

=>200=2*16+(n-1)2
=>2n=170
=>n=85
there fore option 5 is correct

Like? Yes (1) | No   

Sanjoy   9 years AGO

n/2{2*16+(n-1)*2}/n=100
n=85

Like? Yes (1) | No   

Gurram Mahendra ranganath   9 years AGO

using the formula, Sn=n/2[2a+(n-1)d]
n=?,a=16,d=2
=>average = Sn/n=>1/2[2a+(n-1)d]=100
=>n=85.

Like? Yes (1) | No   

Prithwijit Ghosh   9 years AGO

16,18,20,............100,.........180,182,184 average equal to 100

No of numbers is 16 to184
2(8,9,10,12.........92)=85

Like? Yes (1) | No   

Devendra Marghade   9 years AGO

Sum of 'n' terms of arithmetic progression 16,18, 20, 22, 24,.. = (n/2)[2*16+(n-1)2], In order to get the average=100,
(n/2)[2*16+(n-1)2] /n=100
n=85
Answer=Option 5)

Like? Yes (1) | No   

rakesh   9 years AGO

average= (sum of 1st no and last no) / 2.
to get avg of 200 last no should be 184.
So totla even nos from 16 to 184 are 85.

Like? Yes (1) | No   

MRITUNJAY   9 years AGO

let the number of term be n.
100*n=n/2[2a+(n-1)d]
200=[2*16+(n-1)2]
200=32+2n-2
200=30+2n
170=2n
n=85.

Like? Yes (1) | No   

Srinivas   9 years AGO

sum of 85 terms is 8500

Like? Yes (1) | No   

PAWAN KUMAR   9 years AGO

a=16, d=2.Let the no of terms be n.
Then, n/2[2*16 + (n-1)*2] = 100*n
=> n = 0, 85
So, the no of req terms is 85. Ans.

Like? Yes (1) | No   

mukund   9 years AGO

By using ap addition formula. We can get equation
N^2-85n=0
So n=85
Where n= no of terms

Like? Yes (1) | No   

siddharth prakash singh   9 years AGO

let total of n terms is eq.
n/2[32+(n-1)2]=100n
=>n=85

Like? Yes (1) | No   

ABHINAV PUSHPAM   9 years AGO

From options.. And using ap formulas..

Like? Yes (1) | No   

Testing Account   9 years AGO

addition 26 to 34 is to 150
avg is to be 15
addition 36 to 44 and add to previous no. the avg. become 25
we follow this rule so. we on to below conclusion
we continuously solve u get 100-15=85

Like? Yes (1) | No   

sayantani jana   9 years AGO

by solving the problem get,
the numbers of terms are taken is 85

Like? Yes (1) | No   

Neha Garg   9 years AGO

This is an A.P.
sum=100/n
sum=n/2(2a+(n-1)d)
100/n=n/2(32+(n-1)2)
on solving
n=85

Like? Yes (1) | No   

hemanth   9 years AGO

The given Series is in Arithmetic Progression with a = 16, d = 2.
The average of an A.P. is ( 2a + (n-1)d ) / 2.
Here the average is 100, so substituting the values for a = 16 and d =2,
( 2*16 + (n-1)2 ) / 2 = 100
16 + (n-1) = 100
n = 85

So the number of terms required to make the average of 100 for the given sequence is 85.

Like? Yes (1) | No   

KUMAR HARSH   9 years AGO

here the sereis is in AP
let we take n number element
s=n/2[2*16+(n-1)*2]=n(n+15)
given s/n=100=[n(n+15)]/n
n=100-15=85

Like? Yes (1) | No   

Pooja Shaw   9 years AGO

as the average of 1st 10 even numbers starting from 16 is 25 and average of 1st 15 numbers is 30,so according to that after 5 numbers the average is increased by 5. Calculating according to this we get avg of 1st 80 numbers is 95 so avg of 1st 85 numbers will b 100

Like? Yes (1) | No   

Abhik Das   9 years AGO

simply take the total numbers=n
so as it is in AP series so,
n/2*[2*16+(n-1)*2]=100*n
or, 30+2*n=200
or, n=85

Like? Yes (1) | No   

azharshahid01@gmail.com   9 years AGO

100n = n/2(2a+(n-1)d)
here a = 16, d =2
on solving, n = 170

Like? Yes (1) | No   

nishi   9 years AGO

sum of the series/n=100
((n/2)(2*16+(n-1)2))/n=100
n=85

Like? Yes (1) | No   

darshana kumrawat   9 years AGO

n/2(2*16 +(n-1)*2)=n*100
thus n=85

Like? Yes (1) | No   

Subashini.K.J   9 years AGO

avg of sum of a.p= 100=s/n=(2a+(n-1)d)
=(2*16*(85-1)*2)/2=100

Like? Yes (1) | No   

Akila   9 years AGO

Answer should be 85 ,average = sum/number of terms

Like? Yes (1) | No   

Sagar Kumar Subudhi   9 years AGO

let total numbers be 'n' then according to a.p.,the sum of numbers is 100n
we know sum of all numbers in an a.p can be calculated as
S=(n/2)*(2a+(n-1)d)
by putting a=16,d=2 and s=100n we can calculate the value of n

Like? Yes (1) | No   

mehul gandhi   9 years AGO

sum of series 16,18,20,22 ..... which is in AP will be
SUM = (no of terms/2) {2*first term + (no of terms - 1)* comm difference
SUM = (N/2) * {2*16+(N-1)2}

SUM = (N/2) * {30 + 2N} .............................(1)

now according to question , the numbers are to be added in such a way that the average will be 100
i.e.

AVg = (SUM of Numbers/No of terms)
or
AVg = SUM/N
or
SUM = AVg * N ................................................(2)

putting equation (2) into (1)

100 * N = (N/2) * {30 + 2N}
200 = 30 + 2N

or N = 85

Thanks

Like? Yes (1) | No   

jaganmohan rao .pola   9 years AGO

SUM OF =16+18+20+22+24+.........+184 = 8500
TOTAL NO OBESERVATIONS = 85

AVG = SUM/OBE =8500/85 = 100

ANS : 85

Like? Yes (1) | No   

b.subbarao   9 years AGO

16,18,20,22...............n terms
here a=16,d=18-16=2
sum of n =n/2(2a+(n-1))d)
sum of n= n/2(2*16+(n-1))2)
sum of n=n/2(32+2n-2)
=n/2(30+2n)
average=n/2(30+2n)/n=15+n
as per the data average=100
there fore 15+n=100
n=100-15=85
to get average as 100 we have to take 85 numbers in that series
so option (5) is right answer

Like? Yes (1) | No   

ADERU CHENCHU NITHISH   9 years AGO

100=(n/2)*(2a+(n-1)d)*(1/n)
200=32+2(n-1)
84=n-1
n=85

Like? Yes (1) | No   

Dorababu M   9 years AGO

sum of n terms in ap = n/2 (a+l)
last term will be l=a+(n-1)d
then n/2 (a+a+(n-1)d)
average of n terms will be
1/2(2a+(n-1)d)=100
a=16
d=2
30+2n=200
2n=170
n=85

Like? Yes (1) | No   

Pranati Kundu   9 years AGO

sum=100n
100n=n/2[2*16+(n-1)*2]
n=85

Like? Yes (1) | No   

Madhumoy Gope   9 years AGO

Suppose n nos. are required
So,from arithmetic progression we have,
(n/2)*(2*16+(n-1)*2)=100*n
So,n=85

Like? Yes (1) | No   

RAJAT KHANDELWAL   9 years AGO

avg= sum of all nos /n
sum=n/2{2a+(n-1)d}
avg=sum/n=1/2{2*16+(n-1)2}=100
16+(n-1)=100
n=85

Like? Yes (1) | No   

karthik hariharan   9 years AGO

Sum of n numbers = n/2 (2a+(n-1)d)
⇒ 85/2(2*16+(84)2)
⇒ 85/2(32+168)
⇒ 85/2(200) =8500.

Average = 8500/85 =100.

So the answer is 85.

Like? Yes (1) | No   

neha   9 years AGO

average = sum of all terms/ number of terms
let the number of terms=n
first term of an AP(a)=16, (cd)common difference=2
using formula for sum =(n/2)*[(2*a+(n-1)*cd]
sum of terms= (n/2)*(2*16+(n-1)*2)
average=100
hence
100=[(n/2)*(2*16+(n-1)*2)]/n
=> n=85.

Like? Yes (1) | No   

AD.CHNADRA MOHAN   9 years AGO

(16+18)/2=17,(16+18+20)/3=18 ........ we require 85 numbers in a series to get an average of 100 because sequence starts from 16

Like? Yes (1) | No   

RAVI SHANKAR JHA   9 years AGO

for n number of terms the sum is (1st term +n )/2 and for n =85 the average is 100

Like? Yes (1) | No   

Aparna Shukla   9 years AGO

when we add till 89th digit from 16 to 184 we get 8900 as ans and we know avg=8900÷89=100

Like? Yes (1) | No   

prem kishor   9 years AGO

it is a Ap sequence , so for 85 tems sum is 8500. thus the average is 100

Like? Yes (1) | No   

sai   9 years AGO

sum of n numbers =n/2*(2a+9n-1)d)/n =100

Like? Yes (1) | No   

arun v k   9 years AGO

a=16,d=2, n=?

sum of n terms= Sn= (n/2)(2a+(n-1)d)
average=100= Sn/n

n=85

Like? Yes (1) | No   

aditya singh   9 years AGO

let total number is = n
then average of all the number is-
n/2{2a+(n-1)2}=100n
2a+(n-1)d=200
2*16+(n-1)2=200
(n-1)2=200-32
n-1=168/2
n-1=84
n=85

Like? Yes (1) | No   

ilamparithi   9 years AGO

16+18+20+22+.....+176=8500
8500%85=100
No=85

Like? Yes (1) | No   

Meenakshi   9 years AGO

a=16 d=2
its a A.P series
sum of n numbers=n/2(2a+(n-1)d)
=>85/2(2*16+84*2)
=>85/2(32+168)
=>85/2(200)
=>8500
Average=8500/85=>100
so option is 5)85

Like? Yes (1) | No   

PUJA MUKHERJEE   9 years AGO

15+n=100
solving n=85

Like? Yes (1) | No   

ajit kumar sharma   9 years AGO

since given series is in Arithmetic Progression.......we will find the sum of the series by assuming number of terms n....we will equate it to 100*n. and we will get n=85.

Like? Yes (1) | No   

Mahindrakar Dinesh   9 years AGO

Since the given numbers are in arithmetic progression, average would be the middle number. For an instance the average for given 5 numbers wil be the middle number i.e 20. If we add next two numbers then average becomes 22. So to become the average as 100. We should add 80 more numbers. Total 80+5=85

Like? Yes (1) | No   

Vaibhav Srivastava   9 years AGO

average is increases proportional to number of terms increases

Like? Yes (1) | No