Let {Sₙ} denotes sum of n terms of an A.P. If {S_{2n}} = 3{Sₙ} , then ratio frac{{{S_{3n}}}}{{{S

English

Gujarati

Hindi

8. Sequences and Series

easy

Let ${S_n}$ denotes the sum of $n$ terms of an $A.P.$ If ${S_{2n}} = 3{S_n}$, then ratio $\frac{{{S_{3n}}}}{{{S_n}}} = $

A

$4$

B

$6$

C

$8$

D

$10$

Solution

(b) ${S_{2n}} = 3{S_n}$

$ \Rightarrow $ $\frac{{2n}}{2}\{ 2a + (2n – 1)d\} = 3\;.\;\frac{n}{2}\{ 2a + (n – 1)d\} $

$ \Rightarrow $ $2a = (n + 1)d$

Put $2a = (n + 1)d$ in $\frac{{{S_{3n}}}}{{{S_n}}}$,

we get its value $6$.

Standard 11

Mathematics

Share

Similar Questions

Let $x _1, x _2 \ldots ., x _{100}$ be in an arithmetic progression, with $x _1=2$ and their mean equal to $200$ . If $y_i=i\left(x_i-i\right), 1 \leq i \leq 100$, then the mean of $y _1, y _2$, $y _{100}$ is

hard

(JEE MAIN-2023)

If $(b+c),(c+a),(a+b)$ are in $H.P$ , then $a^2,b^2,c^2$ are in…….

normal

Let $S_n$ denote the sum of first $n$ terms an arithmetic progression. If $S_{20}=790$ and $S_{10}=145$, then $S_{15}-$ $S_5$ is:

medium

(JEE MAIN-2024)

Let $3,7,11,15, \ldots, 403$ and $2,5,8,11, \ldots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to…………………

hard

(JEE MAIN-2024)

If ${a_1} = {a_2} = 2,\;{a_n} = {a_{n – 1}} – 1\;(n > 2)$, then ${a_5}$ is

easy