Question

If the n^th term of the AP is 5n+2. What will be the value of n so that the sum of the first n terms is 295?

(a) 9

(b) 10

(c) 11

(d) 4

This question was posed to me during an interview.

Enquiry is from Solution of Quadratic Equation by Factorisation topic in division Quadratic Equation of Mathematics – Class 10

Answer 1

The correct choice is (b) 10

For explanation: The n^th term of the AP is 5n+2.

T1=a=5+2=7

T2=5(2)+2=12

d=T2-T1=12-7=5

Sn=295

Sn=\(\frac {n}{2}\)(2a+(n-1)d)

295=\(\frac {n}{2}\)(2(7)+(n-1)5)

590=14n+5n^2-5n

5n^2+9n-590=0

5n^2+59n-50n-590=0

n(5n+59)-10(5n+59)=0

(n-10)(5n+59)=0

n=10, \(\frac {-59}{5}\)