Question

How do you find the sum of the arithmetic sequence given 26+19+12+5+....(-37)?

Answer 1

The sum of the arithmetic sequence `=-55`

Explanation:

The arithmetic sequence provided is :
`26 + 19 + 12 + 5 + ......-37`

• The first term: `a_1 = 26`

• The common difference for the sequence can be found as follows:
  `a_2 - a_1 = 19 - 26 =-7`
  `color(blue)(d =-7`

• The last term `a_n = -37`

We can find the total number of terms `(n)` of the series by using the formula:
`color(blue)(a_n = a_1 + ( n-1)d`

`-37 = 26 + ( n-1) xx color(blue)((-7))`

`-37 = 26 -7n + 7`

`-37 = 33-7n`

`7n = 33 + 37`

`7n = 70`

`n = 10`

Now we find the sum of the terms applying the below mentioned formula:

`color(green)(S_n = n/2 (a_1 + a _n)`

`=10/2 ( 26 +(-37))`

`=5 xx (-11)`

`=-55`