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:

$\frac{n}{2}[2a+(n-1)d]$

Since, there are 13 terms.

= $\frac{13}{2}[2(51)+(13-1)5]$

= $\frac{13}{2}[102+60]$

= $\frac{13}{2}[162]$

= $13 \times 81$

= 1053

Therefore, the sum of the series is 1053.

So, Option G is the correct answer.