Question

the sum of the frist n terms of an A.p is 3n2 + 5n write A.p hence find its 16th term

Answer 1

hello Kunal

It is Given that

Sn = 3n^2 + 5n

To find out the 16th term, firstly we need to find the first term ( a ) and common difference ( d)

For first term
let n =1

$s1 = 3 ({1}^{2}) + 5(1) = 8$
Hence the first term a = 8

Now let n = 2
$s2 = 3( {2}^{2} ) + 5(2) = 22$
Now second term
= S2 - a
= 22 - 8 = 14

Now we have a and a2, with which we can calculate d

d = a2 - a1

d = 14 - 8 = 6

Now 16th term of the AP

a16 = a + ( n -1 )d

= 8 + 15 ( 6 )
= 98

Hence the 16th term is 98

hope it helps
#jerri