Question

What is the sum of the first thirteen terms in a geometric series with a r = 3 a1= -10

Answer 1

To calculate the sum of the first thirteen terms of the geometric series, we use the formula below.

Formula:

• S₁₃ = a(rⁿ-1)/(r-1).............. Equation 1

Where:

• S₁₃ = Sum of the first thirteen terms of the geometric series.
• a = First term of the series
• r = Common ratio

Given:

• a = -10
• r = 3
• n = 13

Substitute these values into equation 1

• S₁₃ = -10(3¹³-1)/(3-1)
• S₁₃ = -7971615