Convert the recursive form a↓1 = 5, a↓n = 2a↓n-1 to the explicit form.
a. a↓n = 3(7)^n
b. a↓n = 5(2)*n-1
c. a↓n = 5(2)^n+1
d. a↓n = 2(5)^n-1
The recursive form a↓1 = 5, a↓n = 2a↓n-1 states that the first term is 5, and each subsequent term is twice the previous term.
To convert this to the explicit form, we can use the formula for the nth term of a geometric sequence:
a↓n = a↓1 * r^(n-1)
In this case, a↓1 = 5 and r = 2. Substituting these values into the formula, we get:
a↓n = 5 * 2^(n-1)
So the explicit form of the sequence is given by option d: a↓n = 2(5)^n-1.