Question

The sum of the 1st n terms of an AP is given by Sn =2n^2 +3n. Find the 16th term of the AP

Answer 1

a1= s1
a1=2+3
    = 5
a2= s2-s1
    = 14-5
    = 9
d= 9-5 = 4

a16=5+15(4)
      = 65

Answer 2

Hey

Given that :-

Sn = 2n² + 3n

Let n be 1 .

S1 = 2 ( 1 ) ² + 3 ( 1 )

= 2 + 3

= 5 .


Now , S1 = a1

So, a1 = 5 .


So ,

S2 = 2 ( 2 ) ² + 3 ( 2 )

= 2 ( 4 ) + 6

= 8 + 6

= 14 .

So ,

a2 = ( S2 - S1 )

a2 = ( 14 - 5 )

a2 = 9 .

So ,

a1 = 5

a2 = 9

d = ( 9 - 5 ) = 4

Now ,

16th term = a + 15d

= 5 + 15 ( 4 )

= 5 + 60

= 65 .

thanks :)