Which formula can be used to sum the first n terms of a geometric sequence?

To sum the first n terms of a geometric sequence, you can use the formula:

S_n = a(1 – rⁿ) / (1 – r)

In this formula:

• S_n is the sum of the first n terms of the geometric sequence.
• a is the first term of the sequence.
• r is the common ratio (the factor by which each term is multiplied to get the next term).
• n is the number of terms to be summed.

For example, if you have a geometric sequence where the first term is 2 and the common ratio is 3, and you want to find the sum of the first 4 terms, you could plug these values into the formula. The first four terms would be 2, 6, 18, and 54. Using the formula:

S₄ = 2(1 – 3⁴) / (1 – 3)

Calculating this gives:

S₄ = 2(1 – 81) / (-2) = 2(-80) / (-2) = 80

So, the sum of the first 4 terms is 80. This formula provides a quick and efficient way to calculate the sum of a specified number of terms in a geometric sequence without needing to manually add each term.