1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# If the sum of the first $2n$ terms of A.P $2,5,8,\dots$ is equal to the sum of the first $n$ terms of A.P $57,59,61,\dots .$, then $n$ is equal to:

A

$10$

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

$12$

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

$11$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D

$13$

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C $11$Explanation for the correct option.Sum of $n$ terms of AP, ${\mathbit{S}}_{\mathbf{n}}\mathbf{=}\frac{\mathbf{n}}{\mathbf{2}}\mathbf{\left[}\mathbf{2}\mathbf{a}\mathbf{+}\left(n-1\right)\mathbf{d}\mathbf{\right]}$Sum of $2n$ terms of AP $2,5,8,\dots$will be $=\frac{2\mathrm{n}}{2}\left[2\left(2\right)+\left(2\mathrm{n}-1\right)3\right]$ [Here, $a=2,\mathrm{and}d=3$]$=n\left(1+6n\right)$Sum of $n$ terms of AP $57,59,61,\dots .$will be $=\frac{\mathrm{n}}{2}\left[2\left(57\right)+\left(\mathrm{n}-1\right)2\right]$ [Here, $a=57,\mathrm{and}d=2$]$=\frac{n}{2}\left(112+2n\right)\phantom{\rule{0ex}{0ex}}=n\left(56+n\right)$As per the given information, $\begin{array}{rcl}n\left(1+6n\right)& =& n\left(56+n\right)\\ & ⇒& 1+6n=56+n\\ ⇒5n& =& 55\\ ⇒n& =& 11\end{array}$Hence, option C is correct.

Suggest Corrections
23
Join BYJU'S Learning Program
Related Videos
Introduction
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program