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

A geometric progression is a sequence where every term bears a constant ratio to its preceding term.

### Answer: The formula that is used to find the sum the first n terms of a geometric sequence is S_{n} = a(1 - r^{n}) / (1 - r)

Let's look into the solution below.

**Explanation:**

The formula used to calculate the sum of 'n' terms of a geometric sequence is given as,

S_{n} = a(1 - r^{n}) / (1 - r), where r is not equal to 1.

Here,

- 'a' is the first term
- 'r' is the common ratio
- 'n' is the number of terms
- 'S
_{n}' is the sum of 'n' terms

Let's take an example to understand this.

Here is a GP sequence 3, 15, 75, …. Let us calculate the sum of the first 7 terms.

a = 3, r = 5, n = 7

⇒ S_{n} = a (1 - r^{n}) / (1 - r)

⇒ S_{7} = 3 (1 - 5^{7 }) / (1 - 5)

⇒ S_{7 }= 3 × (1 - 78125) / ( - 4)

⇒ S_{7 }= 3 × ( - 78124) / ( - 4)

⇒ S_{7} = 3 × 19531

⇒ S_{7} = 58593

Thus, the sum of the first 7 terms of the given GP is 58593.

### Hence, the sum of 'n' terms of a GP is calculated using S_{n} = a(1 - r^{n}) / (1 - r)

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