Find the sum of a finite arithmetic sequence from n = 1 to n = 18, using the expression 4n - 10.

Solution:

Given the expression of a finite arithmetic sequence is 4n - 10

To find: the sum from n = 1 to 18

To find the sum of the finite arithmetic sequence from the first term to the 18th term, we need to calculate the sum of the first 18 terms by using the sum formula

S\(_n\)= n/2(a + l)

Where a = first term and L = last term

Inorder to find the first term ‘a’, replace n with 1 in a\(_n\) = 4n - 10

So a\(_1\) = 4(1) - 10 = 4 - 10 = -6

To find the last term l, replace n with 18 in a\(_n\) = 4n - 10

So a\(_{18}\)= l = 4(18) - 10

= 72 - 10 = 62

S\(_{18}\) = (18/2)(-6 + 62) = 9 × 56

S\(_{18}\) = 504

Find the sum of a finite arithmetic sequence from n = 1 to n = 18, using the expression 4n - 10.

Summary:

The sum of a finite arithmetic sequence from n = 1 to n = 18, using the expression 4n - 10 is 504