Answer:
- a[n] = -4·(-3)^(n-1); -2916
- a[n] = 12·(1/4)^(n -1); 3/1024
Step-by-step explanation:
You want the explicit formula for each of the geometric sequences, and the 7th term.
- -4, 12, -36
- 12, 3, 3/4
Explicit formula
The explicit formula for a geometric sequence with first term a[1] and common ratio r is ...
a[n] = a[1]·r^(n-1)
1. a[1] = -4, r = -3
The explicit formula is ...
a[n] = -4·(-3)^(n-1)
The 7th term is ...
a[7] = -4·(-3)^(7-1) = -2916
2. a[1] = 12, r = 1/4
The explicit formula is ...
a[n] = 12·(1/4)^(n -1)
The 7th term is ...
a[7] = 12·(1/4)^(7-1) = 3/1024
