Question

If an ap if the sum of first n terms is n square + 2 then its 18th term is

Answer 1

$s _{n} = {n}^{2} + 2 \\ s_{1} =a = {1}^{2} + 2 = 1 + 2 = 3 \\ s_{2} = {2}^{2} + 2 = 4 + 2 = 6 \\ a + a_{2} = 6 \\ 3 + a_{2} = 6 \\ a_{2} = 3 \\ \\ d = a_{2} - a = 3 - 3 = 0 \\ \\ a_{18} = a + (18 - 1)d = 3 + 17(0) = 3 + 0 \\ a_{18} = 3$

Hence, the 18th term of the given A.P. is 3.

Answer 2

sum = n^2 + 2n

sum of 1 term = S1 = 1^2 + 2×1 = 3 = a1

sum of 2 terms = S2 = 2^2 + 2×2 = 8

a1 + a2 = S2 = 8

a2 = 8 - 3 = 5

d = a2 - a1 = 5 - 3 = 2

a18 = a1 + (18 - 1)d

a18 = 3 + 17 × 2 = 37

18th term is 37