Find the sum of the arithmetic sequence. 5, 7, 9, 11,..., 23

Solution:

The sum of the first n terms of an arithmetic sequence is given by the expression:

Sn = n/2[2a + (n-1)d]

Here a = 5, d = 2

The term 23 is the nth term where n is calculated as shown

Tn = a + (n - 1)d = 5 + (n - 1)2

23 = 5 + (n - 1)2

n - 1 = (23 - 5)/2 = 18/2 = 9

n = 10

Therefore the sum of 10 terms is:S₁₀

S₁₀ = 10/2[2(5) + (10 - 1)(2)]

S₁₀ = 5[10 + 9(2)] = 5(28) = 140

Find the sum of the arithmetic sequence. 5, 7, 9, 11,..., 23

Summary:

The sum of the arithmetic sequence 5, 7, 9, 11,..., 23 is 140