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 to the previous 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.

Tags

CCSS.HSA.SSE.B.4

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 + l), where a is the first term, l is the last term, and n is the number of terms.

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 - r^n) / (1 - r), where a is the first term, r is the common ratio, and n is the number of terms.

Tags

CCSS.HSA.SSE.B.4

Front

Evaluate the sum of the geometric series: -1 + 5 - 25 + 125 + ... + 78,125

Back

The sum is 65104.

Tags

CCSS.HSA.SSE.B.4

Front

Evaluate S_8 for the series: 2 + 6 + 10 + 14 + ...

Back

S_8 = 128.

Front

Evaluate S_n for the series: 28 + 35 + 42 + 49 + ..., n = 10

Back

S_n = 595.

Front

What is the common difference in an arithmetic series?

Back

The common difference is the constant amount that each term increases or decreases by in an arithmetic series.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio in a geometric series?

Back

The common ratio is the constant factor by which each term in a geometric series is multiplied to get the next term.

Tags

CCSS.HSF.BF.A.2

Front

Calculate the final sum of the series: 1 + 2 + 3 + 4 + ... + 6

Back

The final sum is 21.