Question

What is the 20th term of the sequence defined by
$\tt a_n = (n − 1) (2 - n) (3 + n)$
​

Answer 1

We need to find 20th term i.e. a20 Let an = (n - 1) (2 - n) (3 + n) putting n = 20 in (1) a20 = (20 - 1) (2 - 20) (3 + 20) = (19) ( -18) (23) = -7866.

Hence the 20th term is -7866.

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Answer 2

$\huge\purple{ \underline{ \boxed{\mathbb{\red{QUESTION : }}}}}$

What is the 20th term of the sequence defined by $\sf a_n = (n − 1) (2 - n) (3 + n)$ ?

$\huge\purple{ \underline{ \boxed{\mathbb{\red{ANSWER : }}}}}$

• The 20th term of the sequence is -7866 .

$\huge\purple{ \underline{ \boxed{\mathbb{\red{EXPLANATION : }}}}}$

$\green{ \large \underline{ \mathbb{\underline{GIVEN : }}}}$

• $\sf a_n = (n − 1) (2 - n) (3 + n)$

$\green{ \large \underline{ \mathbb{\underline{TO \: FIND : }}}}$

• 20th term of the sequence .

$\green{ \large \underline{ \mathbb{\underline{SOLUTION: }}}}$

To get 20th term of the sequence , we put n = 20 in $\sf a_n = (n − 1) (2 - n) (3 + n)$

$\displaystyle \longrightarrow\sf a_{20} = (20 − 1) (2 - 20) (3 + 20) \: \\ \\ \displaystyle \longrightarrow\sf a_{20} =(19)( - 18)(23) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow\sf a_{20} = - 342 \times 23 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \displaystyle \longrightarrow\sf a_{20} = - 7866 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple {\boxed{ \begin{array}{l}\textsf{The 20th term of the sequence is -7866 .}\end{array}}}$