# What is the sum of the first 10 terms of the sequence defined by a_{n }= 2n - 3?

We will use the concept of arithmetic summation in order to find the sum of the first 10 terms.

## Answer: The sum of the first 10 terms of the sequence defined by a_{n }= 2n - 3 is 80.

Let us see how we will use the concept of arithmetic summation in order to find the sum of the first 10 terms.

**Explanation:**

We know that the n^{th} term is given by a_{n} = 2n-3.

When n = 1,

We have a_{1} = 2(1) - 3

Thus, First term = -1

When n = 2, a_{2} = Second term = 2(2) - 3 = 1

When n = 3, a_{3} = Third term = 2(3) - 3 = 3

Thus, the sequence is -1, 1, 3...

We can see that the terms form a series of arithmetic progression with the first term a_{1} = -1 and common difference d = 2.

Sum of 'n' terms of arithemetic progression = (n/2)[2a + (n – 1)d]

On substituting n =10, a = -1, and d = 2 we get sum of the series

(10 / 2) [2(-1) + (10 - 1)(2)]

= 5 [-2 + 18]

= 5 × 16 = 80

### Hence, the sum of first 10 terms of the given sequence is 80.