Arithmetic and Geometric Sequences and Series Flashcard Review

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term (a_n) of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

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

How do you find the nth term of a geometric sequence?

Back

The nth term (a_n) of a geometric sequence can be found using the formula: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Front

What is the formula for 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_n is the nth term.

Front

What is the formula for 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 r is the common ratio and r ≠ 1.

Front

Evaluate the geometric series: 3 + 15 + 75 + 375 + ..., n=6

Back

The sum is 11,718.

Front

Evaluate the geometric series: 1 - 2 + 4 - 8 ..., n=8

Back

The sum is -85.

Front

Find the first four terms of the sequence given the rule: a_n = 4(5)^(n-1)

Back

The first four terms are 4, 20, 100, 500.

Front

Find the 32nd term of the sequence: 34, 37, 40, 43, ...

Back

The 32nd term is 127.