Answer:
f(n) = 10 * 5^(n-1)
an = 15-2.5n
Step-by-step explanation:
{(1, 10), (2, 50), (3, 250), (4, 1250)}
The formula for a geometric sequence is
an = a1 * r ^(n-1)
where a1 is the first term and r is the rate in which it increase
a1 =10
r = 5, each term goes up by a factor of 5
50/10 = 5
250/50 = 5
etc
f(n) = 10 * 5^(n-1)
What is the explicit rule for the sequence?
13, 10.5, 8, 5.5, 3, 0.5, ...
For an arithmetic sequence the formula is
an = a1 + d(n-1)
where a1 is the first term and d is the common difference
a1= 13 and d = -2.5
10.5 -13 = -2.5
8. - 10 = -2.5
etc
an = 13 - 2.5 ( n-1)
Simplifying
an = 13 -2.5n + 2.5
an = 15-2.5n
