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Question

Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.

1 , 5 , 25 , ...

Write your answer using decimals and integers.

an =
(
)n - 1

Answer 1

The sequence given is 1, 5, 25, ...

To find a formula for the \( n \)-th term of this sequence, we can observe the pattern of the terms:

1. The first term (\( a_1 \)) is \( 1 = 5^0 \).
2. The second term (\( a_2 \)) is \( 5 = 5^1 \).
3. The third term (\( a_3 \)) is \( 25 = 5^2 \).

From this pattern, we can see that the \( n \)-th term appears to be \( 5^{(n - 1)} \).

Thus, the formula for the \( n \)-th term is:

\[ a_n = 5^{(n - 1)} \]

where \( n = 1 \) for the first term.