Question

What is the sum of all of the multiples of 7 between 100 and 200?

Answer 1

Using the arithmetic progression

$S_n=\dfrac{a_1+a_n}{2}\cdot n\\a_1=105\\a_n=196\\d=7\\\\a_n=a_1+(n-1)\cdot d\\196=105+(n-1)\cdot 7\\7n-7=91\\7n=98\\n=14\\\\S_{14}=\dfrac{105+196}{2}\cdot 14=2107$