Find the sum of a finite geometric sequence from n = 1 to n = 6, using the expression - 2(5)ⁿ - 1.

Solution:

A Geometric sequence is a sequence in which each term is obtained by multiplying a fixed non-zero real number to the preceding term except the first term. The fixed number is called the common ratio, denoted by r. 

Given the sum of a geometric sequence by the expression - 2(5)ⁿ - 1.

The number of terms is finite ⇒ 6 terms

Here n = 6. Let us substitute n = 6 in the given expression.

S\(_n\) = 2(5)ⁿ - 1 = 2(5)⁶ - 1

= 2 × 15625 -1

= 31250-1

S\(_n\)= 31249

Find the sum of a finite geometric sequence from n = 1 to n = 6, using the expression - 2(5)n - 1.

Summary:

The sum of the first six terms of a finite geometric sequence is 31249.