If a_(1)=5 and a_(n)=na_(n-1)-2 then find the value of a_(3). Answer:

Given information: We are given the first term of the sequence, a_(1)=5, and the recursive formula for the sequence, a_(n)=na_(n-1)-2. To find a_(3), we first need to find a_(2) using the recursive formula.Find a_(2): Using the recursive formula a_(n)=na_(n-1)-2, we substitute n=2 to find a_(2): a_(2) = 2 * a_(1) - 2 a_(2) = 2 * 5 - 2 a_(2) = 10 - 2 a_(2) = 8 Now we have the value of a_(2).Find a_(3): Next, we use the value of a_(2) to find a_(3) using the same recursive formula: a_(3) = 3 * a_(2) - 2 a_(3) = 3 * 8 - 2 a_(3) = 24 - 2 a_(3) = 22 We have now found the value of a_(3).

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If
a_(1)=5 and
a_(n)=na_(n-1)-2 then find the value of
a_(3).
Answer:

If $a_{1}=5$ and $a_{n}=n a_{n-1}-2$ then find the value of $a_{3}$ . $\newline$ Answer:

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Precalculus

Find the roots of factored polynomials

Full solution

Q. If

a_{1}=5

and

a_{n}=n a_{n-1}-2

then find the value of

a_{3}

\newline

Answer:

Given information: We are given the first term of the sequence, $a_{1}=5$ , and the recursive formula for the sequence, $a_{n}=na_{n-1}-2$ . To find $a_{3}$ , we first need to find $a_{2}$ using the recursive formula.
Find $a_{2}$ : Using the recursive formula $a_{n}=na_{n-1}-2$ , we substitute $n=2$ to find $a_{2}$ :
$a_{2} = 2 \times a_{1} - 2$
$a_{2} = 2 \times 5 - 2$
$a_{2} = 10 - 2$
$a_{2} = 8$
Now we have the value of $a_{2}$ .
Find $a_{3}$ : Next, we use the value of $a_{2}$ to find $a_{3}$ using the same recursive formula: $\newline$ $a_{3} = 3 \times a_{2} - 2$ $\newline$ $a_{3} = 3 \times 8 - 2$ $\newline$ $a_{3} = 24 - 2$ $\newline$ $a_{3} = 22$ $\newline$ We have now found the value of $a_{3}$ .