Question

Write the 50^th term of the series 2 + 3 + 6 + 11 + 18 + ………

Answer 1

Let s = 2 + 3 + 6 + 11 + 18 + …………. + n

By shifting each term by one

S = 2 + 3 + 6 + 11 + 18 + ……… + nth ……… (1)

S = 2 + 3 + 6 + 11 + 18 + ……… + (n - 1)th + nth …(2)

by (1) - (2) we get

0 = 2 + 1 + 3 + 5 + 7 + …….nth - (n - 1)th - nth

Nth = 2 + (1 + 3 + 5 + 7 + 9 + …….2r - 1) ……….(3)

Nth = 2 + (summation of first (n - 1)th term)

We know by property that: