Math Homework Help ?

Question

Find the sum of the arithmetic sequence having a1 = 81, an = - 13, n = 20.

Answer 1

The first term of the arithmetic sequence a = a1 = 81

The nth term of the arithmetic sequence an =a + (n - 1)d = -13

The sum of first and nth term of the arithmetic sequence = 2a + (n - 1)d = 81 - 13 = 68

The number of terms in the arithmetic sequence n = 20

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

Substitute n = 20 and 2a + (n - 1)d = 68 in the sum of arithmetic sequence

The sum of the arithmetic sequence = 20 / 2 [68]

Simplify

The sum of the arithmetic sequence = 680.

Answer 2

, ,

Formula for sum of arithmetic sequence

a  = first term and l  = last term.

In this case first term is and last term is .

Substitute the values in

Sum of the arithmetic sequence = 680.