If a_(1)=7 and a_(n)=na_(n-1)+1 then find the value of a_(3). Answer:

Find a_(2): To find a_(3), we first need to find a_(2) using the given recursive formula a_(n)=na_(n-1)+1. We know that a_(1)=7, so we can substitute n=2 into the formula to find a_(2). a_(2) = 2*a_(1) + 1 = 2*7 + 1 = 14 + 1 = 15.Calculate a_(3): Now that we have a_(2), we can use it to find a_(3) using the same recursive formula. Substitute n=3 into the formula to find a_(3). a_(3) = 3*a_(2) + 1 = 3*15 + 1 = 45 + 1 = 46.

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If
a_(1)=7 and
a_(n)=na_(n-1)+1 then find the value of
a_(3).
Answer:

If $a_{1}=7$ and $a_{n}=n a_{n-1}+1$ 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}=7

and

a_{n}=n a_{n-1}+1

then find the value of

a_{3}

\newline

Answer:

Find $a_{2}$ : To find $a_{3}$ , we first need to find $a_{2}$ using the given recursive formula $a_{n}=na_{n-1}+1$ . We know that $a_{1}=7$ , so we can substitute $n=2$ into the formula to find $a_{2}$ . $a_{2} = 2\cdot a_{1} + 1 = 2\cdot 7 + 1 = 14 + 1 = 15$ .
Calculate $a_{3}$ : Now that we have $a_{2}$ , we can use it to find $a_{3}$ using the same recursive formula. $\newline$ Substitute $n=3$ into the formula to find $a_{3}$ . $\newline$ $a_{3} = 3\cdot a_{2} + 1 = 3\cdot 15 + 1 = 45 + 1 = 46$ .