Find the first 4 terms of the geometric sequence for which f\left(1\right)=5f(1)=5 and r=-9r=−9 .

Answer 1

Start by writing down the general form for a geometric sequence:

f(n) = f(1)·r^n-1

1. f(n) is the n^th term in the sequence (n = 1, 2, 3, 4, ...)
2. f(1) is the first term in the sequence = 5
3. r = the common ratio = -9

Now fill in the numbers:

f(n) = f(1)·r^n-1

f(n) = 5·(-9)^n-1

f(1) = 5·(-9)^1-1 = 5·(-9)⁰ = 5

f(2) = 5·(-9)^2-1 = 5·(-9)¹ = -45

f(3) = 5·(-9)^3-1 = ______?

f(4) = _____?

Use your calculator to help.