ssccglapex

If $\mathbf{S}_{\mathbf{n}}$ denotes the sum of the first r terms of an A.P. Then, $\mathbf{S}_{3 \mathrm{n}}:\left(\mathbf{S}_{2 \mathrm{n}}-\mathbf{S}_{\mathbf{n}}\right)$ is

A. n B. 3n C. 3 D. None of these Answer: Option C
Show Answer

Solution(By Apex Team)

$\begin{aligned}S_n&=\frac{n}{2}[2a+(n-1)d]\\ S_{2n}&=\frac{2n}{2}[2a+(2n-1)d]\text{ and }\\ S_{3n}&=\frac{3n}{2}[2a+(3n-1)d]\\ &\text{ Now }S_{2n}-S_n&\\ &=\frac{2n}{2}[2a+(2n-1)d]-\frac{n}{2}[2a+(n-1)d]\\ &=\frac{n}{2}[4a+(4n-2)d]-[2a+(n-1)d]\\ &=\frac{n}{2}[4a-2a+(4n-2-n+1)d]\\ &=\frac{n}{2}[2a+(3n-1)d]\\ &=\frac{1}{3}\left(S_{3n}\right)\\ &\therefore S_{3n}:\left(S_{2n}-S_n\right)\\ &=3:1\text{ or }\frac{3}{1}=3\end{aligned}$

Related Questions On Progressions


How many terms are there in 20, 25, 30 . . . . . . 140?

A. 22
B. 25
C. 23
D. 24
Show Answer

Find the first term of an AP whose 8th and 12th terms are respectively 39 and 59.

A. 5
B. 6
C. 4
D. 3
Show Answer

Find the 15th term of the sequence 20, 15, 10 . . .

A. -45
B. -55
C. -50
D. 0
Show Answer

The sum of the first 16 terms of an AP whose first term and third term are 5 and 15 respectively is

A. 600
B. 765
C. 640
D. 680
Show Answer



More Related Questions On Progressions