Find the sum of the first 6 terms of a geometric sequence

Question

 if the first term is 5 and the common ratio is -4..

Answer 1

Given : Number of terms, n = 6, first term, a₁ = 5 and common ratio, r = - 4.S_n =

The sum of the first n terms of the geometric sequence : S_n = a₁[(1 - rⁿ)/(1 - r)], r ≠ 1.

Substitute the corresponding values.

S₆ = 5[(1 - (- 4)⁶)/(1 - (- 4))]

S₆ = 5[(1 - 4⁶)/(1 + 4)]

S₆ = 5[(1 - 4096)/5]

S₆ = 5[(- 4095)/5]

S₆ = - 4095.

Therefore, the sum of the first 6 terms of the geometric sequence is - 4095.