Question 13

# The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99 is

Solution

S = 7 x 11 + 11 x 15 + 15 x 19 + ...+ 95 x 99

Nth term of the series can be written as $$T_{n} = (4n+3)*(4n+7)$$

Last term, (4n+3) = 95 i.e. n = 23

$$\sum_{n=1}^{n=23} (4n+3)*(4n+7)$$

$$\Rightarrow$$ $$\sum_{n=1}^{n=23}16n^2+40n+21$$

$$\Rightarrow$$ $$16*\dfrac{23*24*47}{6}+40*\dfrac{23*24}{2}+21*23$$

$$\Rightarrow$$ $$80707$$