Question

Write the sum using summation notation, assuming the suggested pattern continues.

-9 - 3 + 3 + 9 + ... + 81

Answer 1

`\sum _(n = 1) ^(18) (6n - 15)`

Step-by-step explanation

The given series

`- 9 - 3 + 3 + 9 + ... + 81`

This is an arithmetic series with a common difference of

`d = - 3 - - 9 = 6`

The first term of the series is:

`a_1 = - 9`

The general term is given by:

`a_n =a_1 + d(n - 1)`

`a_n = - 9+ 6(n - 1)`

`a_n = - 9+ 6n - 6`

`a_n =6n - 15`

The last term is 81

We can use this to determine the number of terms in the series.

`81=6n - 15`

`81 + 15=6n`

`6n = 96`

`n = (96)/(6) = 16`

The summation notation is:

`\sum _(n = 1) ^(18) (6n - 15)`