Question

Write a recursive formula for the sequence

1, 3, 9, 27, 81, . . . a1 = 1

Answer 1

for all sequences, always check the difference between each successsive number to identify the pattern

Answer 2

\[\sum_{n=0}^{\infty} (3)^n\]

Answer 3

\[a_{n} = r (a_{n - 1})\]
where:
r = common ratio
so, to find the common ratio we do the following:
\[r = \frac{ a _{n} }{ a _{n-1} } = \frac{ 3 }{ 1 } = 3\]
\[r = \frac{ a _{n} }{ a _{n-1} } = \frac{ 9 }{ 3 } = 3\]
\[r = \frac{ a _{n} }{ a _{n-1} } = \frac{ 27 }{ 9 } = 3\]
So we can conclude that the common ratio is 3.
\[a_{n} = 3(a_{n-1})\]

Answer 4

so your recursive formula for the sequence would be:
\[a_{n} = 3(a_{n - 1})\]