CBSE BoardEnglish MediumSTD 10MathsArithmetic Progressions1 Mark
MCQ
$(5 + 13 + 21 + .... + 181) = ?$
A
$2476$
B
$2337$
C
$2219$
✓
$2139$
✓
Answer
Correct option: D.
$2139$
Let a be the term and $d$ be the common difference.
$5 + 13 + 21 +... + 181$
$a = 5$ and $d = 13 - 5 = 8$
$a_n= a + (n -1)d$
$\Rightarrow 181 = 5 + (n -1)8$
$\Rightarrow 176 = 8n - 8$
$\Rightarrow 8n = 184$
$\Rightarrow n = 23$
$\text{S}_\text{n}=\frac{23}{2} \ [$frist term $+$ last term$]$
$\Rightarrow\text{S}_\text{n}=\frac{23}{2}[5+181]$
$\Rightarrow\text{S}_\text{n}=\frac{23}{2}[186]$
$\Rightarrow\text{S}_\text{n}=2139$
So, the sum is $2139.$
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