Question

Use summation notation to write the series 49 + 54 + 59 +... for 14 terms.

Answer 1

Summation notation to write the series 49 + 54 + 59 +... for 14 terms is attached .
I hope that will help.

Answer 2

Arithmetic sequence states that a sequence of numbers such that the difference between the consecutive terms is constant.

it is given by:
`a_n = a+(n-1)d` where a is the first term , n is the number of term and d is the common difference.

Given the series:
`49 + 54 + 59+ ......`

here, Common difference(d) = 5

First term(a) = 49

by definition we have;

For nth term

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

`a_n = 49+(n-1)5`

`a_n =49+5n -5` = 5n + 44

To write the series using summation notation for 14 terms

Summation symbol
`'\sum'`

The series for 14th terms is given by;

`\sum_(n=1)^(14)(5n +44)`