# What is the sum of the arithmetic sequence 3, 9, 15..., if there are 22 terms?

**Solution:**

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

First term, a = 3

Common difference, d = 9 - 3

d = 6

We have to find the sum of 22 terms.

The sum of the n terms of arithmetic sequence is given by

[latex]s_{n}=\frac{n}{2}(a+l)[/latex]

Where, n = number of terms

a = first term

l = last term

The n-th term of an arithmetic sequence is given by a_{n} = a + (n - 1)d

[latex]a_{22}=3+(22-1)(6)[/latex]

[latex]a_{22}=3+(21)(6)[/latex]

[latex]a_{22}=3+126[/latex]

[latex]a_{22}=129[/latex]

Now, a=3, l=129, n=22

[latex]s_{22}=\frac{22}{2}(3+129)[/latex]

[latex]s_{22}=11(132)[/latex]

[latex]s_{22}=1452[/latex]

Therefore, the sum upto 22 terms is 1452.

## What is the sum of the arithmetic sequence 3, 9, 15..., if there are 22 terms?

**Summary:**

The sum of the arithmetic sequence 3, 9, 15..., if there are 22 terms is 1452.

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