Question

if sn=2nsquare + 3n find a16

Answer 1

sn = 2n^2 + 3n
s1 = 2(1^2) + 3(1) = 5
a = 5. eq.1
n = 16
sn = 2n^2 + 3n
n/2 (2a + (n-1)(d)) = 2n^2 + 3n
n( 2a + (n-1)(d)) = 4n^2 + 6n
n(2a + (n-1)(d)) = n(4n + 6)
2a + (n-1)(d) = 4n + 6
a + (n-1)(d) = 4n + 6 - a
an = 4n + 6 - a
a16 = 4(16) + 6 - 5. {a=5}from eq.1
a16 = 64 +1
a16 = 65