Geometric Sequences

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

Front

What is the common ratio (r) in a geometric sequence?

Back

The common ratio (r) is the factor by which we multiply each term to get the next term in a geometric sequence.

Front

Find the first four terms of the sequence given the rule: a(0)= 10; a(n) = 3 a(n-1)

Back

10, 30, 90, 270

Front

Write the explicit formula for the geometric sequence: 3, -12, 48, -192, ...

Back

a(n) = 3(-4)^n

Front

Find the next three terms: -4, -12, -36, -108, ...

Back

-324, -972, -2916

Front

Find the 11th term for: 64, -32, 16, -8, …

Back

0.0625

Front

What does r represent in the explicit formula for a geometric sequence?

Back

Common Ratio

Front

How do you find the nth term of a geometric sequence?

Back

Use the formula a(n) = a(0) * r^n, where a(0) is the first term and r is the common ratio.

Front

If the first term of a geometric sequence is 5 and the common ratio is 2, what is the 4th term?

Back

The 4th term is 5 * 2^3 = 40.

Front

What is the formula for the sum of the first n terms of a geometric sequence?

Back

S_n = a(0) * (1 - r^n) / (1 - r) for r ≠ 1.