Question

Write the sum using summation notation, assuming the suggested pattern continues.
-9 - 3 + 3 + 9 + ... + 81

Answer 1

ANSWER

$\sum _{n = 1} ^{18} (6n - 15)$

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.

$81=6n - 15$

$81 + 15=6n$

$6n = 96$

$n = \frac{96}{6} = 16$

The summation notation is:

$\sum _{n = 1} ^{18} (6n - 15)$