Write the first five terms of the following sequence and obtain the corresponding series :
$a_{1}=3, a_{n}=3 a_{n-1}+2$ for all $n\,>\,1$
Write the first five terms of the following sequence and obtain the corresponding series :
$a_{1}=3, a_{n}=3 a_{n-1}+2$ for all $n\,>\,1$
$a_{1}=3, a_{n}=3 a_{n-1}+2$ for $n\,>\,1$
$\Rightarrow a_{2}=3 a_{1}+2=3(3)+2=11$
$a_{3}=3 a_{2}+2=3(11)+2=35$
$a_{4}=3 a_{3}+2=3(35)+2=107$
$a_{5}=3 a_{4}+2=3(107)+2=323$
Hence, the first five terms of the sequence are $3,11,35,107$ and $323$
The corresponding series is $3+11+35+107+323+\ldots$
Similar Questions
If ${a^2},\;{b^2},\;{c^2}$ are in $A.P.$, then ${(b + c)^{ - 1}},\;{(c + a)^{ - 1}}$ and ${(a + b)^{ - 1}}$ will be in
If ${a^2},\;{b^2},\;{c^2}$ are in $A.P.$, then ${(b + c)^{ - 1}},\;{(c + a)^{ - 1}}$ and ${(a + b)^{ - 1}}$ will be in
Given sum of the first $n$ terms of an $A.P.$ is $2n + 3n^2.$ Another $A.P.$ is formed with the same first term and double of the common difference, the sum of $n$ terms of the new $A.P.$ is
Given sum of the first $n$ terms of an $A.P.$ is $2n + 3n^2.$ Another $A.P.$ is formed with the same first term and double of the common difference, the sum of $n$ terms of the new $A.P.$ is
- [JEE MAIN 2013]
If $a_1, a_2, a_3, …….$ are in $A.P.$ such that $a_1 + a_7 + a_{16} = 40$, then the sum of the first $15$ terms of this $A.P.$ is
If $a_1, a_2, a_3, …….$ are in $A.P.$ such that $a_1 + a_7 + a_{16} = 40$, then the sum of the first $15$ terms of this $A.P.$ is
- [JEE MAIN 2019]
In an $\mathrm{A.P.}$ if $m^{\text {th }}$ term is $n$ and the $n^{\text {th }}$ term is $m,$ where $m \neq n$, find the ${p^{th}}$ term.
In an $\mathrm{A.P.}$ if $m^{\text {th }}$ term is $n$ and the $n^{\text {th }}$ term is $m,$ where $m \neq n$, find the ${p^{th}}$ term.
Let $a$, $b$ be two non-zero real numbers. If $p$ and $r$ are the roots of the equation $x ^{2}-8 ax +2 a =0$ and $q$ and $s$ are the roots of the equation $x^{2}+12 b x+6 b$ $=0$, such that $\frac{1}{ p }, \frac{1}{ q }, \frac{1}{ r }, \frac{1}{ s }$ are in A.P., then $a ^{-1}- b ^{-1}$ is equal to $......$
Let $a$, $b$ be two non-zero real numbers. If $p$ and $r$ are the roots of the equation $x ^{2}-8 ax +2 a =0$ and $q$ and $s$ are the roots of the equation $x^{2}+12 b x+6 b$ $=0$, such that $\frac{1}{ p }, \frac{1}{ q }, \frac{1}{ r }, \frac{1}{ s }$ are in A.P., then $a ^{-1}- b ^{-1}$ is equal to $......$
- [JEE MAIN 2022]