What is the sixth term of following series: 2+2i, 5+3i, 10+5i, 17+7i, 26+11i, ......

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08 May 2017 Series

What is the sixth term of following series:
2+2i, 5+3i, 10+5i, 17+7i, 26+11i, ......

OPtion

1) 36+17i
2) 36+15i
3) 36+13i
4) 35+13i
5) 37+13i
6) 37+15i
7) 37+17i
8) 36+19i
9) 35+15i
10) None of these

Solution

Lets represent each term of series x+iy
x and y are two different series as described below:
x = Square of natural numbers + 1 = (1+1), (4+1), (9+1), (16+1), (25+1), (36+1)
y= Prime numbers Series = 2, 3, 5, 7, 11, 13

So the 6th term is = [(6^2+1) + (6th Prime number)i = 37+13i

Correct Option: 5 Best Solution (15)

SAYAN CHATTERJEE   7 years AGO

The real part of the nos .are 2, 5, 10, 17, 26......So common difference being on AP, comes out to be 11....And the real part becomes 26+11=37,
The coeff.s of the imaginary part are the prime numbers.....So the 6 th prime is 13..
So the term becomes 37+13i.....
Option 5.

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Haritha Mummidivarapu   7 years AGO

a+bi ,
here a is sum of previous number +consecutive odd number
b is consecutive prime number
so option 5

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Bupathikavya   7 years AGO

Series is ----- (n^2 +1) + nth prime(i)

Therefore 6th term is 6^2 + 1 +6th prime(i)
37 +13i

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G.S.Kantharao   7 years AGO

2+2i,5+3i,10+5i,17+7i,26+11i
The first terms in the terms of series=2,(2+3),(5+5),(10+7),(17+9),(26+11)...…
The second term in the series of terms is =2i,3i,5i,7i,11i,13i .....All these are with a prime number series.
Hence the correct answer is5.

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palak Jain   7 years AGO

2,5,10,17,26,,,,have a difference of 3,5,7,9,,,so next no 26+11=37

Imaginary nos are prime nos 2,3,5,7,11,,, next would be 13
So sixth term is 37+13i

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Mukund Manohar   7 years AGO

Numbers with i part :-
Prime Numbers
So, 6th term of i part is 13i
Number without i part :-
Double Difference Series
2,5,10,17,26
5-2 =3
10-5=5
17-10=7
26-17=9
Now, 5-3 = 2
7-5 = 2
9-7 = 2
So, 6th term without i part = (9+2) + 26 = 37
6th term of given series is 37+13i

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Amarnath Kumar Upadhyay   7 years AGO

2 ,5 ,10, 17 , 26
Difference of two consecutive term form AP of 3 5 7 9 11 with cd 2
so 6th term integer part is 26+11=37
now complex part is prime no series so prime no after 11 is 13 so
6th term coplex part is 13i
so overall 6th term is 37 + 13i

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MENKA MAURYA   7 years AGO

First term - 2+3=5,5+5=10,10+7=17,17+9=26,26+11=37.Second term- 2i,3i,5i,7i,11i all terms are odd.Therefore,next term will 13i.Required answer is 37+13i

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jyothi chhabria   7 years AGO

real part is implementation of 3,5,7,9 ,11
imaginary part is the prime number sequence 2,3,5,7,11,13
so next term is 26+11+13i=37+13i

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madhuri   7 years AGO

Real part has the sequence of difference of 3,5,7,9, so dixth term will have the difference of 11..so by adding 11 to 26 we get 37.
Imaginary part has the sequence of prime numbers 2,3,5,7,11 .so sixth term will be surely 13.
so the answer is 37+13i

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Monil Shah   7 years AGO

Here first term in a+bi that is a is obtained by adding 3,5,7,...
and b is prime numbers...hence next term would be 37+13i

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Lokesh Reddy    7 years AGO

the series follows a digit and thereafter adding odd number to it along with prime digits are multiplied with i and added to it....

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Vahira Bollina   7 years AGO

here ist term difference is 3,5,7,9 and next 11
2nd term difference 2,3,5,7,11,--prime numbers
so, next term is 13
(26+11)+13i=37+13i

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Bhavika Valiveti   7 years AGO

real part differ by odd series I.e.,3,5,7...and imaginary part is the sequence of prime numbers...

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donthula manasa   7 years AGO

2+2i,5+3i,10+5i,17+7i,26+11i
2,5,10,17,26 consider the difference:3,5,7,9
so next difference is 11.
therefore 26+11=37
2i,3i,5i,7i,11i these all are prime numbers.
so next prime number is 13i

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