Question

Write and explicit formula for the geometric sequence
25,5,1,1/5

Answer 1

The explicit formula for the geometric sequence 25, 5, 1, 1/5 is an = 25 * (1/5)n-1.

Step-by-step explanation:

To find the explicit formula for a geometric sequence, we need to find the common ratio and the first term. In this sequence, the common ratio is obtained by dividing each term by the previous term. In this case, to get from 25 to 5, we divide by 5, and to get from 5 to 1, we divide by 5 again. Therefore, the common ratio is 1/5.

Since the first term is 25, we can write the explicit formula as:

an = 25 * (1/5)n-1

This formula gives us the nth term of the sequence, where n represents the position of the term.

Answer 2

a(n) = a(0) x (1/5)^(n)
Where (n) is the term number and a(0) is the first term
For example,
a(1) = 25(1/5)
= 5
a(2) = 25(1/5)²
= 1
And so on