What is the sum of the geometric sequence 1, -6, 36, … if there are 6 terms?

Solution:

Sum of n terms of geometric progression = S_n = a(1 - rⁿ)/(1 - r)

Given geometric sequence is 1, -6, 36, …

Here, first term(a) = 1,

Common ratio(r) = -6/1

⇒ r = -6

Number of terms(n) = 6

S_n = a(1 - rⁿ)/(1 - r)

S₆ = 1(1 - (-6)⁶)/ (1 - (-6))

S₆ = 1 × ( 1 - 46656 ) / 1 + 6

S₆ = 1 × (-46655) / 7

S₆ = -6665

Therefore, the sum of the geometric sequence is S₆ = -6665.

What is the sum of the geometric sequence 1, -6, 36, … if there are 6 terms?

Summary:

The sum of 6 terms of the given geometric sequence 1, -6, 36, … is S₆ = -6665.