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.
$5+13+21+\ldots+181$
$a=5 \text { and } d=13-5=8$
$a_n=a+(n-1) d$
$\Rightarrow 181=5+(n-1) 8$
$\Rightarrow 176=8 n-8$
$\Rightarrow 8 n=184$
$\Rightarrow n=23$
$\text{S}_\text{n}=\frac{23}{2}$ [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 $2139.$
$5+13+21+\ldots+181$
$a=5 \text { and } d=13-5=8$
$a_n=a+(n-1) d$
$\Rightarrow 181=5+(n-1) 8$
$\Rightarrow 176=8 n-8$
$\Rightarrow 8 n=184$
$\Rightarrow n=23$
$\text{S}_\text{n}=\frac{23}{2}$ [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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