Question

If t_n denotes the nth term of the series 2 + 3 + 6 + 11 + 18 + ... then t₅₀ is ______.

Options

• 49² – 1

• 49²

• 50² + 1

• 49² + 2

Answer 1

If t_n denotes the nth term of the series 2 + 3 + 6 + 11 + 18 + ... then t₅₀ is 49² + 2.

Explanation:

Let S_n = 2 + 3 + 6 + 11 + 18 + … + t₅₀

Using method of difference, we get

S_n = 2 + 3 + 6 + 11 + 18 + … + t₅₀

And S_n = 0 + 2 + 3 + 6 + 11 + … + t₄₉ + t₅₀

Subtracting equation (ii) from equation (i), we get

0 = 2 + 1 + 3 + 5 + 7 + … – t₅₀ terms

⇒ t₅₀ = 2 + (1 + 3 + 5 + 7 + … upto 49 terms)

⇒ t₅₀ = `2 + 49/2 [2 xx 1 + (49 - 1)2]`

= `2 + 49/2 [2 + 96]`

= `2 + 49/2 xx 98`

= `2 + 49 xx 49`

= 49² + 2