If a_(1)=9 and a_(n+1)=5a_(n)+3 then find the value of a_(5). Answer:

Given Information: We are given the first term of the sequence, a_(1)=9, and the recursive formula a_(n+1)=5a_(n)+3. To find a_(5), we need to find the values of a_(2), a_(3), and a_(4) first, using the recursive formula.Find a_(2): Let's find a_(2) using the recursive formula: a_(2) = 5a_(1) + 3 = 5*9 + 3 = 45 + 3 = 48.Find a_(3): Now, let's find a_(3) using the recursive formula: a_(3) = 5a_(2) + 3 = 5*48 + 3 = 240 + 3 = 243.Find a_(4): Next, we find a_(4) using the recursive formula: a_(4) = 5a_(3) + 3 = 5*243 + 3 = 1215 + 3 = 1218.Find a_(5): Finally, we find a_(5) using the recursive formula: a_(5) = 5a_(4) + 3 = 5*1218 + 3 = 6090 + 3 = 6093.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

If
a_(1)=9 and
a_(n+1)=5a_(n)+3 then find the value of
a_(5).
Answer:

If $a_{1}=9$ and $a_{n+1}=5 a_{n}+3$ then find the value of $a_{5}$ . $\newline$ Answer:

View step-by-step help

Home

Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. If

a_{1}=9

and

a_{n+1}=5 a_{n}+3

then find the value of

a_{5}

\newline

Answer:

Given Information: We are given the first term of the sequence, $a_{1}=9$ , and the recursive formula $a_{n+1}=5a_{n}+3$ . To find $a_{5}$ , we need to find the values of $a_{2}$ , $a_{3}$ , and $a_{4}$ first, using the recursive formula.
Find $a_{2}$ : Let's find $a_{2}$ using the recursive formula: $\newline$ $a_{2} = 5a_{1} + 3 = 5\times9 + 3 = 45 + 3 = 48$ .
Find $a_{3}$ : Now, let's find $a_{3}$ using the recursive formula: $\newline$ $a_{3} = 5a_{2} + 3 = 5\times48 + 3 = 240 + 3 = 243$ .
Find $a_{4}$ : Next, we find $a_{4}$ using the recursive formula: $\newline$ $a_{4} = 5a_{3} + 3 = 5\times243 + 3 = 1215 + 3 = 1218$ .
Find $a_{5}$ : Finally, we find $a_{5}$ using the recursive formula: $\newline$ $a_{5} = 5a_{4} + 3 = 5\times1218 + 3 = 6090 + 3 = 6093$ .