Question

Question 2 (ii)
Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5.

Answer 1

Multiples of 2 as well as of 5 from 1 to 500 are 10, 20, 30, …. 500.
$\therefore$ a = 10, d = 10, $a_n$ = l = 500
$\because$ 500 = 10 + (n - 1) 10
$\Rightarrow$ 490 = (n - 1) 10
$\Rightarrow$ n - 1 = 49 $\Rightarrow$ n = 50
$\Rightarrow$ n - 1 = 49 $\Rightarrow$ n = 50
$\because S_n=\frac{n}{2}(a+l)$
$\Rightarrow S_{50}=\frac{50}{2}(10+500)=\frac{50}{2}\times 510$
$=50\times 255=12750$