Search any question & find its solution
Question:
Answered & Verified by Expert
It the sum of first 10 terms of an arithmetic progression with first term $p$ and common difference $q$, is 4 times the sum of the first 5 terms, then what is the ratio $p: q$ ?
Options:
Solution:
2870 Upvotes
Verified Answer
The correct answer is:
$1: 2$
Since first term $=\mathrm{p}$ and common difference $=\mathrm{q}$. Sum of first 10 terms $=\frac{10}{2}[2 \mathrm{p}+(10-1) \mathrm{q}]$ and
Sum of first 5 terms $=\frac{5}{2}[2 \mathrm{p}+(5-1) \mathrm{q}]$ According to question, $\frac{10}{2}[2 p+9 q]=4 \times \frac{5}{2}[2 p+4 q]$
$\Rightarrow 2 \mathrm{p}+9 \mathrm{q}=4 \mathrm{p}+8 \mathrm{q}$
$\Rightarrow 2 \mathrm{p}=\mathrm{q}$
$\Rightarrow \mathrm{p}: \mathrm{q}=1: 2$
Sum of first 5 terms $=\frac{5}{2}[2 \mathrm{p}+(5-1) \mathrm{q}]$ According to question, $\frac{10}{2}[2 p+9 q]=4 \times \frac{5}{2}[2 p+4 q]$
$\Rightarrow 2 \mathrm{p}+9 \mathrm{q}=4 \mathrm{p}+8 \mathrm{q}$
$\Rightarrow 2 \mathrm{p}=\mathrm{q}$
$\Rightarrow \mathrm{p}: \mathrm{q}=1: 2$
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.