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

When the ratio between any two consecutive terms in a sequence is the same, it is called a geometric progression.

## Answer: The sum of the geometric progression 1, −6, 36, … if there are 6 terms is -6665.

Go through the step-by-step solution to find the sum of 6 terms.

**Explanation:**

The general term of any geometric progression = a r^{(n-1)}

a = 1st term = 1

r = Common ratio = -6

n = Number of terms = 6

Sum of geometric progression with common ratio r can be calculated using the formula

⇒ S_{n} = a (1 - r^{n }) / 1 - r

⇒ S_{6} = 1 (1 - ( -6 )^{6 }) / 1 - ( -6 )

⇒ S_{6 }= 1 × ( 1 - 46656 ) / 1 + 6

⇒ S_{6 }= 1 × (-46655) / 7

⇒ S_{6} = -6665