Consider a sequence that follows a times 5 pattern: 1, 5, 25, 125, ...

a. Write a formula for the nnth term of the sequence. Be sure to specify what value of n your formula starts with.

Answer: Hello mate!

Here we have the sequence: 1, 5, 25, 125, ... etc

the first term is an 1 = 5^0

the second term is 5 = 5^1

the third term is 25 = (5*5) = 5^2

the fourth term is 125 = 5*25 = (5*5*5) = 5^3

then the n-th term is five to the power of (n - 1)

The n-th term of the sequence is:

p (n) = 5^ (n-1)

and the recursive relation is:

p (n) = 5p (n-1)

where p (1) = 1

where n ≥ 1