The sum of first n terms of an AP is given by S_{n} = 2n^{2} + 3n. Find the sixteenth term of the AP.

### Answer

S_{n} = 2n^{2} + 3n

S_{1} = 5 = a_{1}

S_{2} = a_{1} + a_{2} = 14

a_{2} = 9

d = a_{2} – a_{1} = 4

a_{16} = a_{1} + 15d

a_{16} = 5 + 15(4) = 65