We have to determine the value of [tex]\sum _{m=9} ^{21} (5m+6)[/tex]
= (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:
[tex]\frac{n}{2}[2a+(n-1)d][/tex]
Since, there are 13 terms.
= [tex]\frac{13}{2}[2(51)+(13-1)5][/tex]
= [tex]\frac{13}{2}[102+60][/tex]
= [tex]\frac{13}{2}[162][/tex]
= [tex]13 \times 81[/tex]
= 1053
Therefore, the sum of the series is 1053.
So, Option G is the correct answer.
