# What is the sum of the arithmetic sequence 8, 14, 20, …, if there are 24 terms?

An arithmetic progression is a sequence where the differences between every two consecutive terms are the same.

## Answer: The sum of the arithmetic sequence 8, 14, 20, …, up to 24 terms is S_{n }= 1848.

Let us find the sum of the given arithmetic sequence.

**Explanation:**

The sum of the first n terms of an arithmetic sequence when the n^{th} term is NOT known is:

\(S_{n}\)_{ }= n/2 [2a + (n−1)d]

Here, the arithmetic sequence is 8, 14, 20 …,

a = 8

d = \(a_{2}\) - \(a_{1}\) = 14 - 8 = 6

and given that number of terms is 24, so,

n = 24

\(S_{n}\)_{ }= n/2 [2a + (n−1)d]

\(S_{n}\)_{ }= (24/2) [ 2(8) + (24 - 1)(6) ]

\(S_{n}\)_{ }= 12 [ 16 + 23 × 6 ]

\(S_{n}\)_{ }= 12 [ 154 ]

\(S_{n}\)_{ }= 1848