Calculate the sum of all natural numbers between $1$ and $100$ (both inclusive) that are exactly divisible by $7$.
Answer Key:
735
Step-by-Step Solution & Explanation
The numbers are $7, 14, 21, \dots, 98$.
This is an arithmetic progression with first term $a = 7$, common difference $d = 7$, last term $l = 98$.
Number of terms $n = \frac{98 - 7}{7} + 1 = 14$.
Sum $S_n$:
$S_n = \frac{n}{2} (a + l) = \frac{14}{2} (7 + 98) = 7 \times 105 = 735$