Which recursive sequence would produce the sequence 3,13,63,dots ? a_(1)=3 and a_(n)=5a_(n-1)-2 a_(1)=3 and a_(n)=-5a_(n-1)+6 a_(1)=3 and a_(n)=-2a_(n-1)+5 a_(1)=3 and a_(n)=6a_(n-1)-5

Test First Option: Let's start by testing the first option: a_(1)=3 and a_(n)=5a_(n-1)-2 We know the first term a_(1) is 3. Let's find the second term a_(2) using the recursive formula. a_(2) = 5a_(1) - 2 = 5*3 - 2 = 15 - 2 = 13 This matches the second term of the given sequence.Find Second Term: Now let's find the third term a_(3) using the same recursive formula. a_(3) = 5a_(2) - 2 = 5*13 - 2 = 65 - 2 = 63 This matches the third term of the given sequence.Find Third Term: Since the first three terms of the sequence match the given sequence using the first recursive formula, we can conclude that the correct recursive sequence is: a_(1)=3 and a_(n)=5a_(n-1)-2

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which recursive sequence would produce the sequence
3,13,63,dots ?

a_(1)=3 and
a_(n)=5a_(n-1)-2

a_(1)=3 and
a_(n)=-5a_(n-1)+6

a_(1)=3 and
a_(n)=-2a_(n-1)+5

a_(1)=3 and
a_(n)=6a_(n-1)-5

Which recursive sequence would produce the sequence $3,13,63, \ldots$ ? $\newline$ $a_{1}=3$ and $a_{n}=5 a_{n-1}-2$ $\newline$ $a_{1}=3$ and $a_{n}=-5 a_{n-1}+6$ $\newline$ $a_{1}=3$ and $a_{n}=-2 a_{n-1}+5$ $\newline$ $a_{1}=3$ and $a_{n}=6 a_{n-1}-5$

View step-by-step help

Home

Math Problems

Precalculus

Identify arithmetic and geometric series

Full solution

Q. Which recursive sequence would produce the sequence

3,13,63, \ldots

\newline

a_{1}=3

and

a_{n}=5 a_{n-1}-2

\newline

a_{1}=3

and

a_{n}=-5 a_{n-1}+6

\newline

a_{1}=3

and

a_{n}=-2 a_{n-1}+5

\newline

a_{1}=3

and

a_{n}=6 a_{n-1}-5

Test First Option: Let's start by testing the first option: $\newline$ $a_{1}=3$ and $a_{n}=5a_{n-1}-2$ $\newline$ We know the first term $a_{1}$ is $3$ . Let's find the second term $a_{2}$ using the recursive formula. $\newline$ $a_{2} = 5a_{1} - 2 = 5\times3 - 2 = 15 - 2 = 13$ $\newline$ This matches the second term of the given sequence.
Find Second Term: Now let's find the third term $a_{3}$ using the same recursive formula. $\newline$ $a_{3} = 5a_{2} - 2 = 5\times13 - 2 = 65 - 2 = 63$ $\newline$ This matches the third term of the given sequence.
Find Third Term: Since the first three terms of the sequence match the given sequence using the first recursive formula, we can conclude that the correct recursive sequence is: $\newline$ $a_{1}=3$ and $a_{n}=5a_{n-1}-2$