Question

the sum of first n terms of an AP is given by sn =2n² + 3n find the sixteenth term of AP

Answer 1

Sn = 2n²+3n
S1 = 5=a1
S2=a1+a2=14=a2=9
D=a2-a1=4
A16=a1+15d
=5+15(4)=65

Answer 2

Sn = 2n^2 + 3n

am = 16

a1 = s1 = 2 + 3 = 5

a1 + a2 = s2 = 8 + 12= 20

a2 = s2 - s1 = 20 - 5 = 1 5

d = 15

am = 6 + ( m -1 ) 15=16

6 + 15m - 15 = 16

16 - 6 + 15m - 15=0

10 + 15m - 5

15m - 5 + 10

15m - 15

m = 1