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Allisa [31]
3 years ago
13

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

Mathematics
1 answer:
Lina20 [59]3 years ago
4 0

<u>ANSWER</u>

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

<u>EXPLANATION</u>

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)

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