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

Find a_(2): To find a_(3), we first need to find a_(2) using the recursive formula a_(n)=na_(n-1)-5. We know that a_(1)=5, so we can substitute n=2 into the formula to get a_(2). a_(2) = 2*a_(1) - 5 a_(2) = 2*5 - 5 a_(2) = 10 - 5 a_(2) = 5Calculate a_(3): Now that we have a_(2), we can find a_(3) using the same recursive formula. Substitute n=3 into the formula to get a_(3). a_(3) = 3*a_(2) - 5 a_(3) = 3*5 - 5 a_(3) = 15 - 5 a_(3) = 10

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

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

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Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. If

a_{1}=5

and

a_{n}=n a_{n-1}-5

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 recursive formula $a_{n}=na_{n-1}-5$ . $\newline$ We know that $a_{1}=5$ , so we can substitute $n=2$ into the formula to get $a_{2}$ . $\newline$ $a_{2} = 2\cdot a_{1} - 5$ $\newline$ $a_{2} = 2\cdot 5 - 5$ $\newline$ $a_{2} = 10 - 5$ $\newline$ $a_{3}$ $0$
Calculate $a_{3}$ : Now that we have $a_{2}$ , we can find $a_{3}$ using the same recursive formula. $\newline$ Substitute $n=3$ into the formula to get $a_{3}$ . $\newline$ $a_{3} = 3\cdot a_{2} - 5$ $\newline$ $a_{3} = 3\cdot 5 - 5$ $\newline$ $a_{3} = 15 - 5$ $\newline$ $a_{3} = 10$