Find the indicated terms in each of the following sequences whose nth terms are:
$ a_{n}=(n-1)(2-n)(3+n) ; a_{1}, a_{2}, a_{3} $

Given:

$a_{n}=(n-1)(2-n)(3+n)$

To do:

We have to find $a_{1}, a_2$ and $a_{3}$.

Solution:

 To find $a_{1}$, we have to substitute $1$ in place of $n$ in $a_{n}=(n-1)(2-n)(3+n)$.

This implies,

$a_{1}=(1-1)(2-1)(3+1)$

$=0(1)(4)$

$=0$.

 To find $a_{2}$, we have to substitute $2$ in place of $n$ in $a_{n}=(n-1)(2-n)(3+n)$.

This implies,

$a_{2}=(2-1)(2-2)(3+2)$

$=1(0)(5)$

$=0$.

To find $a_{3}$, we have to substitute $3$ in place of $n$ in $a_{n}=(n-1)(2-n)(3+n)$.

This implies,

$a_{3}=(3-1)(2-3)(3+3)$

$=2(-1)(6)$

$=-12$.

Therefore, $a_{1}=0, a_{2}=0$ and $a_{3}=-12$. 

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Updated on: 10-Oct-2022

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