Question

iven the recursive formula for the geometric sequence a1=5
, an=2/5an−1
, find the second term of the sequence.(1 point)
Responses

a2=8/5
a subscript 2 baseline equals Start Fraction 8 over 5 End Fraction

a2=2/5
a subscript 2 baseline equals Start Fraction 2 over 5 End Fraction

a2=2
a subscript 2 baseline equals 2

a2=5 2/5
a subscript 2 baseline equals 5 Start Fraction 2 over 5 End Fraction

Answer 1

To find the second term of the geometric sequence defined by the recursive formula

\[
a_1 = 5,
\]
\[
a_n = \frac{2}{5} a_{n-1},
\]

we need to calculate \( a_2 \) using the formula for \( n = 2 \):

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

Substituting \( a_1 \):

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

Now, simplifying:

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

Thus, the second term of the sequence is \(\boxed{2}\).