# Find the sum of the arithmetic sequence.

## 5, 7, 9, 11, ..., 23

+1 vote

The arithmetic series is 5, 7, 9, 11, ........., 23.

First u have to determine the no. of terms that can be done by using

Tn = [a + (n - 1)d]

Tn-------nth term

a---------first term

n---------no.of terms in the series

d---------common difference

here a = 5,d = 2.

let it contain n terms Tn= [a + (n-1)d]

Substitute Tn, a, and d in the equation

23 = 5 + (n - 1)2

Subtract 5 from each side.

18 = (n-1)2

Divide each side by 2

(n - 1) = 9

n = 9 + 1 = 10

The sum of the arithmetic sequence formula: Sn= (n/2)[2a+(n-1)d]

Substitute Sn, a, n and d in the equation

Sn= (10/2)[2(5) + (10-1)2]

Sn= (5)[10 + (9)2]

Sn= 5[10 + 18]

Sn= 5[28] = 140

Therefore the sum of the arithmetic sequence is 140.

The arithmetic sequence : 5,7,9,11....23

The first term of the arithmetic sequence a = 5

The number of terms in the arithmetic sequence : n =10

The common diference of two terms : d = 2

The sum of arithmetic sequence : S = n / 2[2a + (n - 1)d]

Substitute n = 10, a = 5 and d = 2 in the sum of sequence

S = 10 / 2[2(5) + (10 - 1)2]

S = 5[10 + 18]

S = 5[28]

S = 140

The sum of the arithmetic sequence = 140.