Latest TCS Aptitude Question SOLUTION: The sum of 5 numbers in AP is 30 and the sum of their square is 220. Which of the following is the third term ? 1) 5 2) 6 3) 8 4) 9

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The sum of 5 numbers in AP is 30 and the sum of their square is 220.
Which of the following is the third term ?

1) 5
2) 6
3) 8
4) 9

Asked In TCS Pranav Bharti (9 years ago)

Unsolved Read Solution (13)

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Read Solution (13) :

Priya Pandey  (9 years ago)

answer can be easily found in this way-
5 terms of an A.P can be represented in the form as a-2d,a-d,a,a+d,a+2d.
then sum = a-2d + a-d + a + a+2d +a+d that is 30
so after addind a = 6.
that is answer

Is this solution Helpfull? Yes (35) | No (4)  

Aditya keri  (9 years ago)

We have to find the third term. To do so, the formula for nth term in a series is : a + (n-1)d
So, for the third term, substitute n = 3 in the above formula, you get : a + 2d (This is what we need to find)
Now, according to the given question :
Sum of 5 numbers of an AP = 30
So, using the formula n/2(2a + (n-1)d) = 30
Solve the above equation, you get a + 2d = 6
Which is our required answer.

Is this solution Helpfull? Yes (26) | No (1)  

VIKASH KUMAR  (9 years ago)

2+4+6+8+10=30
4+16+36+64+100=220

Is this solution Helpfull? Yes (15) | No (6)  

anupama kumari  (9 years ago)

let the no be a-2d,a-d,a,a+d,a+2d
sum of a-2d+a-d+a+a+d+a+2d=30
5a=30 =>a=6
sum their squares (a-2d)^2+(a-d)^2+a^2+(a+d)^2+(a+2d)^2=220
180+10d^2=220
10d^2=40
d=2
so the nos are 2,4,6,8,10
the third term is 6
ANS=6

Is this solution Helpfull? Yes (8) | No   

venika  (9 years ago)

x+2x+3x+4x+5x=30
15x=30
x=2
sub x value in 3rd term so the answer will be 6

Is this solution Helpfull? Yes (6) | No   

SAHELI BISHNU  (9 years ago)

5/2(2a+4d)=30 ; a+2d=6 Therefore a=2 and d=2 (only possible combination ).
third term is 6

Is this solution Helpfull? Yes (1) | No   

Rajanikanta Pradhan  (8 years ago)

Let the 5 no which are in ap as
A-2d A-d A A+d A+2d
Sum is 30 so 5A = 30
A= 6 which is 3rd no

Is this solution Helpfull? Yes (1) | No   

shuvodeep roy  (9 years ago)

ans will be 6..

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swati priya  (9 years ago)

3rd trm will be 6

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Sumeet  (8 years ago)

let the terms are a-5d,a-3d,a,a+3d,a+5d
sum =>5a=30
=>a=6
therefore 3rd term is 6

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C.G.Kavya sree  (8 years ago)

Sn=n/2[2a+(n-1)d]
S5=5/2[2a+4d]=30
2a+4d=12
a+2d=6 which is the third term

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BOORGU NIKHIL  (8 years ago)

consider a,a+d,a+2d,a+3d,a+4d are 5 numbers in ap
given the sum that 30 we know when sum is given the formula is n/2(2a+(n-1)d)

n/2(2a+(n-1)d)=30
5/2(2a+4d)=30
2a+4d=12
a+2d=6
in the above series a+2d is the third term so the third term is equal to 6
so answer is 2)6

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Vijay  (7 years ago)

a,a+d,a+2d,a+3d,a+4d=30
mean=a+2d=30/5
3rd term=6

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