Question

Find the sum of the series 1 + 4 + 7 + 10 + …. + x = 715

Answer 1

Note: The sum of the series is already provided in the question. The solution to find x is given below.

Let there be n terms in the series.

x = 1 + (n – 1)3

= 3n – 2

Let S be the sum of the series

S = n/2[[1+x] = 715

⇒ n[1 + 3n – 2] = 1430

⇒ n + 3n² – 2n = 1430

⇒ 3n² – n – 1430 = 0

Applying Sri Dhar Acharya formula, we get

⇒ n = 22 as n cannot be a fraction

Therefore x = 3 × 22 – 2 = 64

The value of x is 64