Answer:
\(a_n = 0.5 \cdot 4^{n-1}\)
Step-by-step explanation:
The explicit formula for the nth term of the geometric sequence is given by:
\(a_n = a_1 \cdot r^{n-1}\) ....[1]
As per the statement:
A geometric sequence is defined recursively by:
\(a_n = 4 \cdot a_{n-1}\) ....[2]
The 1st term of the sequence is 0.5
⇒\(a_1 = 0.5\)
We know that:
the recursive formula for geometric sequence is given by:
\(a_n = r \cdot a_{n-1}\) where, r is the common ratio
Compare with [2] we have;
r = 4
Substitute the values of r = 4 and \(a_1 = 0.5\) in [1] we have;
\(a_n = 0.5 \cdot 4^{n-1}\)
Therefore, the explicit formula for the nth term of the sequence is, \(a_n = 0.5 \cdot 4^{n-1}\)
