Arithmetic and Geometric Series Practice

Front

What is an arithmetic series?

Back

An arithmetic series is the sum of the terms of an arithmetic sequence, where each term after the first is obtained by adding a constant difference (d) to the previous term.

Front

How do you find the sum of the first n terms of an arithmetic series?

Back

The sum S_n of the first n terms of an arithmetic series can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where a_1 is the first term and a_n is the nth term.

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 obtained by multiplying the previous term by a constant ratio (r).

Tags

CCSS.HSA.SSE.B.4

Front

How do you find the sum of the first n terms of a geometric series?

Back

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

Tags

CCSS.HSA.SSE.B.4

Front

What is the common difference in an arithmetic sequence?

Back

The common difference (d) in an arithmetic sequence is the constant amount that is added to each term to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in a geometric sequence?

Back

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

Tags

CCSS.HSF.BF.A.2

Front

Evaluate S_12 for the arithmetic series where a_1 = ?, a_12 = 48, and d = 4.

Back

S_12 = 312.

Front

To find the next term in an arithmetic sequence, you...

Back

add the common difference d.

Tags

CCSS.HSF.BF.A.2

Front

To find the next term in a geometric sequence, you...

Back

multiply by the common ratio r.

Tags

CCSS.HSF.BF.A.2

Front

Find S_6 for the geometric series: (-4/5) + 8 + (-80) + 800 + ....

Back

S_6 = 72,727.2.

Tags

CCSS.HSA.SSE.B.4