Geometric Sequences

Front

What is a geometric sequence?

Back

A sequence of numbers in which the ratio between any two consecutive terms is the same.

Front

What is the common ratio in a geometric sequence?

Back

The ratio between any two consecutive terms in a geometric sequence.

Front

What is the first term in a sequence using subscripted notation called?

Back

u₁

Front

Which of the following is a geometric sequence? 1, 4, 7, 10, ...; 1, 2, 6, 24, ...; 1, 1, 2, 3, ...; 1, 3, 9, 27, ...

Back

1, 3, 9, 27, ...

Front

What is the term used for the ratio between two numbers in a geometric sequence?

Back

Common Ratio

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the second term?

Back

6

Front

If the first term of a geometric sequence is 5 and the common ratio is -1, what is the third term?

Back

-5

Front

What is the formula for the nth term of a geometric sequence?

Back

a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

In a geometric sequence, if the first term is 4 and the common ratio is 3, what is the fourth term?

Back

108

Front

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

Back

S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.