Question

In an ap, the sum of the first n terms is 5n^2 + 2n. find the 15th term

Answer 1

S=5n^2+2n
Sum of first2terms = 5(2)^2+ 2(2)
=20+4=24
Sum of first 3 terms = 5(3)^2+2(3)
= 45+6 =51
Sum of first 4terms = 5(4)^2+2(4)
=80+8 =88

Difference between Sum of 3 terms and Sum of two terms = 3rd term of ap= 51-24 =27

Difference between Sum of 4terms and Sum of 3terms = 4th term of ap

= 88-51= 37

3rd term of given ap = 27
4th term = 37
d = t4-t3 = 10
T3= 27
a+2d =27
a+ 2(10) =27
a=27-20
a=7

T15= a+14d
=7+14(10)
=147

T15=147