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 formula for the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be found using the formula: t(n) = a * r^(n-1), where 'a' is the first term and 'r' is the common ratio.

Front

How do you find the common ratio in a geometric sequence?

Back

The common ratio (r) can be found by dividing any term by the previous term: r = a(n) / a(n-1).

Front

What is the recursive formula for a geometric sequence?

Back

The recursive formula for a geometric sequence is: a(n) = a(n-1) * r, where 'r' is the common ratio.

Front

Given the sequence: 3, 6, 12, 24, ..., what is the common ratio?

Back

The common ratio is 2.

Front

Given the sequence: 81, 27, 9, 3, ..., write the explicit rule.

Back

The explicit rule is t(n) = 81 * (1/3)^(n-1).

Front

What is the 5th term of the sequence: 5, 10, 20, 40, ...?

Back

The 5th term is 80.

Front

If the first term of a geometric sequence is 10 and the common ratio is 2, what is the 4th term?

Back

The 4th term is 80.

Front

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

Back

The sum of the first n terms (S_n) of a geometric sequence is given by: S_n = a * (1 - r^n) / (1 - r), where 'a' is the first term and 'r' is the common ratio.

Front

What is the 11th term of the sequence: 64, -32, 16, -8, ...?

Back

The 11th term is 0.0625.