Geometric Series

Front

What is a geometric series?

Back

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

Tags

CCSS.HSA.SSE.B.4

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.

Tags

CCSS.HSF.BF.A.2

Front

How do you find the first four terms of a geometric sequence given a formula?

Back

Substitute n = 1, 2, 3, and 4 into the formula a_n to find the first four terms.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in a geometric sequence?

Back

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

Tags

CCSS.HSF.BF.A.2

Front

Is the sequence {14, 22, 30, 38, ...} arithmetic or geometric?

Back

It is an arithmetic sequence with a common difference (d) of 8.

Tags

CCSS.HSF.BF.A.2

Front

What is the explicit formula for the geometric sequence with a first term of 3 and a common ratio of -4?

Back

The explicit formula is a_n = 3 * (-4)^(n-1).

Tags

CCSS.HSF.BF.A.2

Front

How do you determine if a sequence is arithmetic, geometric, or neither?

Back

A sequence is arithmetic if the difference between consecutive terms is constant, geometric if the ratio of consecutive terms is constant, and neither if neither condition holds.

Tags

CCSS.HSF.BF.A.2

Front

If Daisy received $2 on her first birthday and the amount tripled each year, how much will she receive on her 5th birthday?

Back

She will receive $2 * 3^4 on her 5th birthday.

Tags

CCSS.HSF.BF.A.2

Front

What are the next three terms in the geometric sequence: 512, 256, 128, ...?

Back

The next three terms are 64, 32, and 16.

Tags

CCSS.HSF.BF.A.2

Front

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

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 not equal to 1.

Tags

CCSS.HSA.SSE.B.4