# Math Help - AP prob

1. ## AP prob

the sum of n terms of an AP is $3n^2 +5$. Find the number of terms which equals $159.$

2. Originally Posted by banku12
the sum of n terms of an AP is $3n^2 +5$. Find the number of terms which equals $159.$
hi

T_n=a+(n-1)d=159 ---1

We need to find a and d .

a=S1=3(1)^2+5=8

$T_2=S_2-S_1$

$
=3(2)^2+5-8
$

=9

so a=8 , and the common difference , d=1 . Now substitute into 1 to find n .