What is the sum of the first 10 terms of the sequence defined by a_n = 2n - 3

Solution:

It is given that

a_n = 2n - 3

If n = 1,

a₁ = 2(1) - 3 = 2 - 3 = -1

First term is -1.

If n = 2,

a₂ = 2(2) - 3 = 4 - 3 = 1

Second term is 1.

If n = 3,

a₃= 2(3) - 3 = 6 - 3 = 3

Third term is 3.

So the sequence is -1, 1, 3 ….

We observe that the series are in arithmetic progression with a₁ = -1 and difference d = 2

The formula for the sum of n terms is

Sn = (n/2)[2a + (n – 1)d]

We know that

n =10, a = -1, and d = 2

Substituting the values

S₁₀ = (10 / 2) [2(-1) + (10 - 1)(2)]

S₁₀ = 5 [-2 + 18]

S₁₀ = 5 × 16 = 80

Therefore, the sum of the first ten terms is 80.