Which recursive sequence would produce the sequence 8,37,153,dots ? a_(1)=8 and a_(n)=4a_(n-1)+5 a_(1)=8 and a_(n)=5a_(n-1)+4 a_(1)=8 and a_(n)=-3a_(n-1)+5 a_(1)=8 and a_(n)=5a_(n-1)-3

Check First Option: Let's start by checking the first option: a_(1)=8 and a_(n)=4a_(n-1)+5 We know the first term a_(1) is 8. Let's find the second term using the given recursive formula. a_(2)=4a_(1)+5 a_(2)=4*8+5 a_(2)=32+5 a_(2)=37Find Second Term: Now let's find the third term using the same formula. a_(3)=4a_(2)+5 a_(3)=4*37+5 a_(3)=148+5 a_(3)=153Find Third Term: Since the given sequence is 8, 37, 153, and we have found that the recursive formula a_(n)=4a_(n-1)+5 produces the same sequence for the first three terms, we can conclude that this is the correct recursive sequence.

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Which recursive sequence would produce the sequence
8,37,153,dots ?

a_(1)=8 and
a_(n)=4a_(n-1)+5

a_(1)=8 and
a_(n)=5a_(n-1)+4

a_(1)=8 and
a_(n)=-3a_(n-1)+5

a_(1)=8 and
a_(n)=5a_(n-1)-3

Which recursive sequence would produce the sequence $8,37,153, \ldots$ ? $\newline$ $a_{1}=8$ and $a_{n}=4 a_{n-1}+5$ $\newline$ $a_{1}=8$ and $a_{n}=5 a_{n-1}+4$ $\newline$ $a_{1}=8$ and $a_{n}=-3 a_{n-1}+5$ $\newline$ $a_{1}=8$ and $a_{n}=5 a_{n-1}-3$

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Math Problems

Grade 8

Domain and range of functions

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Q. Which recursive sequence would produce the sequence

8,37,153, \ldots

\newline

a_{1}=8

and

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

\newline

a_{1}=8

and

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

\newline

a_{1}=8

and

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

\newline

a_{1}=8

and

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

Check First Option: Let's start by checking the first option: $\newline$ $a_{1}=8$ and $\newline$ $a_{n}=4a_{n-1}+5$ $\newline$ We know the first term $a_{1}$ is $8$ . Let's find the second term using the given recursive formula. $\newline$ $a_{2}=4a_{1}+5$ $\newline$ $a_{2}=4\times 8+5$ $\newline$ $a_{2}=32+5$ $\newline$ $a_{2}=37$
Find Second Term: Now let's find the third term using the same formula. $\newline$ $a_{3}=4a_{2}+5$ $\newline$ $a_{3}=4\times37+5$ $\newline$ $a_{3}=148+5$ $\newline$ $a_{3}=153$
Find Third Term: Since the given sequence is $8, 37, 153$ , and we have found that the recursive formula $a_{n}=4a_{n-1}+5$ produces the same sequence for the first three terms, we can conclude that this is the correct recursive sequence.