# What is the sum of the arithmetic sequence 3, 9, 15..., if there are 26 terms?

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

## Answer: The sum of the first 26 terms of the arithmetic sequence 3, 9, 15, ...... is 2028.

Let us find the sum of the given arithmetic sequence.

**Explanation: **

Given arithmetic sequence is 3, 9, 15,.....

⇒ a = 3 [first term]

⇒ d = \(a_{2}\) - \(a_{1}\) = 9 - 3 = 6 [common difference]

The number of terms is 26 [Given]

⇒ n = 26

Given that the above sequence is an arithmetic progression.

To find the sum of the n terms, we will use the formula,

\(S_{n}\)_{ }= n/2 [2a + (n−1)d]

By substituting the values in the formula, we get,

\(S_{26}\) = ( 26 / 2 ) [ 2 × (3) + (26 - 1) (6) ]

\(S_{26}\)_{ }= 13 [ 6 + 25 × 6 ]

\(S_{26}\)= 13 [ 6 + 150 ]

\(S_{26}\) = 13 [ 156 ]

\(S_{26}\)_{ }= 2028

We can use the online arithmetic sequence calculator to calculate the sum of 'n' terms of an arithmetic sequence.