Final answer:
To complete the recursive formula of g(n), g(1) is calculated as 60 by substituting n with 1 into the given function. The missing factor to multiply g(n-1) to get g(n) is identified as (3/4), resulting in the formula g(n) = g(n-1) × (3/4).
Step-by-step explanation:
The question involves completing a recursive formula for a function g(n). Given the initial term of the sequence and the common ratio, we can find the missing parts of the formula.
The recursive function is given as g(n) = 80(3/4)^n and g(1) needs to be calculated. The formula also needs a factor to multiply g(n-1) to get g(n).
First, to find g(1), we simply substitute n with 1 into the function:
g(1) = 80(3/4)^1 = 80 * 3/4 = 60
Next, we can identify that the function multiplies each term by (3/4) to get the next term. Therefore, the missing part for multiplying g(n-1) is (3/4).
So, the complete recursive formula is:
- g(1) = 60
- g(n) = g(n-1) × (3/4)