Question

Given the recursive formula for the geometric sequence \(a_1=5\), \(a_n=\frac{2}{5}a_{n-1}\),
find the second term of the sequence. (1 point)
\(a_2=2\)
\(a_2=\frac{2}{5}\)
\(a_2=5\frac{2}{5}\)
\(a_2=\frac{8}{5}\)

Answer 1

To find the second term \(a_2\) of the geometric sequence defined by the recursive formula \(a_n = \frac{2}{5}a_{n-1}\) with the initial term \(a_1 = 5\), we start by calculating \(a_2\):

\[
a_2 = \frac{2}{5} a_1
\]

Substituting the value of \(a_1\):

\[
a_2 = \frac{2}{5} \times 5
\]

Now, simplifying that:

\[
a_2 = 2
\]

Thus, the second term of the sequence is \(a_2 = 2\).

So, the answer is:

\[
\boxed{2}
\]