Question

How do I work this out?

Answer 1

We have to determine the value of
`\sum _(m=9) ^(21) (5m+6)`

= (5(9)+6) + (5(10)+6) +(5(11)+6) + .......... + (5(21)+6)

= 51+56+61+66+ ........ + 111

Since, the common difference is 5, hence this series is in arithmetic progression.

Sum of AP is given by the formula:

`(n)/(2)[2a+(n-1)d]`

Since, there are 13 terms.

=
`(13)/(2)[2(51)+(13-1)5]`

=
`(13)/(2)[102+60]`

=
`(13)/(2)[162]`

=
`13 * 81`

= 1053

Therefore, the sum of the series is 1053.

So, Option G is the correct answer.