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:

∑axⁿ + bx^{n - 1} + cx^{n - 2}…….d₀=a∑xⁿ + b∑x^{n - 1} + c∑x^{n - 2}…….. + d₀∑1

Therefore,

Since,

Thus from (3)

Nth = 2 + (n - 1)²

Hence 50^th term be

50^th = 2 + (50 - 1)²

50^th = 2 + (49)²