Unit 8 - Arithmetic and Geometric Series

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 the formula for the sum of the first n terms of an arithmetic series?

Back

The formula is: S_n = \frac{n}{2} (2a + (n-1)d), where S_n is the sum, a is the first term, d is the common difference, and n is the number of terms.

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.

Front

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

Back

The formula is: S_n = a \frac{1 - r^n}{1 - r}, where S_n is the sum, a is the first term, r is the common ratio, and n is the number of terms.

Front

What is the formula for the sum of an infinite geometric series?

Back

The formula is: S = \frac{a}{1 - r}, where S is the sum, a is the first term, and r is the common ratio (|r| < 1).

Front

Evaluate the series: 4 + 1 + \frac{1}{4} + \frac{1}{16} + ... for n=34.

Back

The sum is \frac{16}{3}.

Front

A sequence has a first term of -21 and a common difference of 8. Find the sum of the first 50 terms.

Back

The sum is 8750.

Front

A sequence has a first term of 7 and a common ratio of -2. Find the sum of the first 6 terms.

Back

The sum is -147.

Front

Find the sum of the infinite geometric series: 16 - 12 + 9 - \frac{27}{4} + ...

Back

The sum is \frac{64}{7}.

Front

Zahid counts jars of marbles: 1, 3, 9, ... If there are 10 jars, how many total marbles?

Back

The total is 29,524.