Search any question & find its solution
Question:
Answered & Verified by Expert
If $a_1, a_2, a_3, \ldots, a_n, \ldots$. are in A.P. such that $a_4-a_7$ $+a_{10}=m$, then the sum of first 13 terms of this A.P., is :
Options:
Solution:
1238 Upvotes
Verified Answer
The correct answer is:
$13 \mathrm{~m}$
$13 \mathrm{~m}$
If $d$ be the common difference, then
$$
\begin{aligned}
m & =a_4-a_7+a_{10}=a_4-a_7+a_7+3 \mathrm{~d}=a_7 \\
\mathrm{~S}_{13} & =\frac{13}{2}\left[a_1+a_{13}\right]=\frac{13}{2}\left[a_1+a_7+6 d\right] \\
& =\frac{13}{2}\left[2 a_7\right]=13 a_7=13 \mathrm{~m}
\end{aligned}
$$
$$
\begin{aligned}
m & =a_4-a_7+a_{10}=a_4-a_7+a_7+3 \mathrm{~d}=a_7 \\
\mathrm{~S}_{13} & =\frac{13}{2}\left[a_1+a_{13}\right]=\frac{13}{2}\left[a_1+a_7+6 d\right] \\
& =\frac{13}{2}\left[2 a_7\right]=13 a_7=13 \mathrm{~m}
\end{aligned}
$$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.