Geometric sequence

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

Front

If the first term of a geometric sequence is 5 and the common ratio is 3, what is the 4th term?

Back

The 4th term is 5 * 3^(4-1) = 5 * 27 = 135.

Front

What is the common ratio in the geometric sequence 2, 6, 18, 54?

Back

The common ratio is 3, as each term is multiplied by 3 to get the next term.

Front

How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of consecutive terms is constant.

Front

What is the common ratio of the geometric sequence 10, 5, 2.5, 1.25?

Back

The common ratio is 0.5, as each term is multiplied by 0.5 to get the next term.

Front

What is the 5th term of a geometric sequence with a first term of 4 and a common ratio of 2?

Back

The 5th term is 4 * 2^(5-1) = 4 * 16 = 64.

Front

What is the difference between an arithmetic sequence and a geometric sequence?

Back

In an arithmetic sequence, each term is obtained by adding a constant (common difference), while in a geometric sequence, each term is obtained by multiplying by a constant (common ratio).

Front

If a geometric sequence has a first term of 8 and a common ratio of 1/2, what is the 6th term?

Back

The 6th term is 8 * (1/2)^(6-1) = 8 * (1/32) = 0.25.

Front

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

Back

The sum S_n of the first n terms can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where r is the common ratio and r ≠ 1.