Question

For a sequence (t_n), if S_n = 5(2ⁿ - 1) then t_n = ______.

विकल्प

• 5 (2ⁿ⁺¹)

• `(5 xx 2^"n")/4`

• 5 (2^n-1)

• `(2 xx (2^("n-1")))/5`

Answer 1

For a sequence (t_n), if S_n = 5(2ⁿ - 1) then t_n = 5 (2^n-1).

Explanation:

We have, S_n = 5(2ⁿ - 1)

We know that, `"a"_"n" = "S"_"n" - "S"_("n - 1")`

= 5(2ⁿ - 1) - 5(2^n-1 - 1)

= 5(2ⁿ - 2^n-1)

= 5(2^n-1)