CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions1 Mark
MCQ
The sum of first $20$ odd natural numbers is :
A
$100$
B
$210$
✓
$400$
D
$420$
✓
Answer
Correct option: C.
$400$
The first $20$ odd no, is given by :
$\{1, 3, 5, 7, 9, 11, ....,37, 39\}$
These form an $A.P.,$ where
$a_1= 1, d = 2, n = 20$
So,
$\text{S}_\text{n}=\frac{\text{n}}{2}[2\text{a}+(\text{n}-1)\text{d}]$
$\text{S}_{20}=\frac{20}{2}[2(1)+(20-1)2]$
$=\frac{20}{2}[2+(19\times2)]$
$=10[2+38]$
$=10\times40$
$\therefore\ \text{S}_{20}=400$
The sum of first $20$ odd no. is $400$.
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