Browse Questions

# What is the sum of all odd natural numbers till 200 ?

(a) 18000 (b) 5000 (c) 10000 (d) 19900

Toolbox:
• Sum of an AP is given by $S_{n} = \large \frac {n}{2} [2a + (n-1)d]$
• nth term of an AP is given by $T_{n} = \large a + (n-1)d$
Sum of an AP is given by $S_{n} = \large \frac {n}{2} [2a + (n-1)d]$
Here $a = 1, \quad d = 2, \quad T_{n} = 199$
$T_{n} = a + (n-1)d$
$\therefore 199 = 1 + (n - 1)2 \implies 198 = (n - 1)2 \implies n = 100$

$S_{n} = \large \frac {n}{2} [2a + (n-1)d]$

$S_{n} = \large \frac {100}{2} [2 X 1 + (100 - 1) X 2]$

$S_{n} = 10000$