Given the recursive formula for the geometric sequence a1=5, an=2/5an-1, Find the second term of the sequence

Answer 1

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

1. The first term \( a_1 = 5 \).
2. To find the second term \( a_2 \), we apply the recursive formula: \[ a_2 = \frac{2}{5} a_1 \] Substituting \( a_1 \) into the formula: \[ a_2 = \frac{2}{5} \cdot 5 \] Simplifying: \[ a_2 = \frac{2 \cdot 5}{5} = 2 \]

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