If a_(1)=6 and a_(n)=-4a_(n-1)-5 then find the value of a_(3). Answer:

Find a_(2): To find the value of a_(3), we need to first find the value of a_(2) using the recursive formula a_(n)=-4a_(n-1)-5, where n represents the term number in the sequence. Given that a_(1)=6, we can substitute n=2 into the formula to find a_(2). Calculation: a_(2) = -4a_(1) - 5 = -4(6) - 5 = -24 - 5 = -29Calculate a_(2): Now that we have the value of a_(2), we can use it to find the value of a_(3) using the same recursive formula. Substitute n=3 into the formula using the value of a_(2) we just found. Calculation: a_(3) = -4a_(2) - 5 = -4(-29) - 5 = 116 - 5 = 111

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
a_(1)=6 and
a_(n)=-4a_(n-1)-5 then find the value of
a_(3).
Answer:

If $a_{1}=6$ and $a_{n}=-4 a_{n-1}-5$ then find the value of $a_{3}$ . $\newline$ Answer:

View step-by-step help

Home

Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. If

a_{1}=6

and

a_{n}=-4 a_{n-1}-5

then find the value of

a_{3}

\newline

Answer:

Find $a_{2}$ : To find the value of $a_{3}$ , we need to first find the value of $a_{2}$ using the recursive formula $a_{n}=-4a_{n-1}-5$ , where $n$ represents the term number in the sequence. $\newline$ Given that $a_{1}=6$ , we can substitute $n=2$ into the formula to find $a_{2}$ . $\newline$ Calculation: $a_{2} = -4a_{1} - 5 = -4(6) - 5 = -24 - 5 = -29$
Calculate $a_{2}$ : Now that we have the value of $a_{2}$ , we can use it to find the value of $a_{3}$ using the same recursive formula. $\newline$ Substitute $n=3$ into the formula using the value of $a_{2}$ we just found. $\newline$ Calculation: $a_{3} = -4a_{2} - 5 = -4(-29) - 5 = 116 - 5 = 111$