Answer:
f(7) = 1.08
Step-by-step explanation:
Given that:
f(5) = 12
A geometric sequence that is defined recursively by the formula
\(f(n) = 0.3 \cdot f(n-1)\) .....[1 ] where, n is an integer and n> 0.
Substitute n = 6 in [1] we have;
\(f(6) = 0.3 \cdot f(5)\)
Using f(5) = 12 we have;
\(f(6) = 0.3 \cdot 12\)
⇒\(f(6) =3.6\)
We have to find f(7).
Substitute n = 7 in [1] we have;
\(f(7) = 0.3 \cdot f(6)\)
Substitute the given values f(6) = 3.6 we have;
\(f(7) = 0.3 \cdot 3.6\)
Simplify:
f(7) = 1.08
Therefore, the value of f(7)to the nearest hundredth is, 1.08