Question

Find the sum of all integers between 50 and 500 which are divisible by 7.

Answer 1

The integers between 50 and 500 that are divisible by 7 are:
56, 63...497
Here, we have:
$$\begin{gathered} a=56 \\ d=7 \\ {a}_n=497 \\ \Rightarrow 56+(n-1)7=497 \\ \Rightarrow 7n-7=441 \\ \Rightarrow 7n=448 \\ \Rightarrow n=64 \\ {S}_n=\frac{n}{2}\left[2a+(n-1)d\right] \\ \Rightarrow S_{64}=\frac{64}{2}\left[2\times 56+(64-1)7\right] \\ \Rightarrow S_{64}=32\left[2\times 56+63\times 7\right]=17696 \end{gathered}$$