Arithmetic and Geometric Sequence and Series Flashcard

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

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term 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

What is the formula for the nth term of a geometric sequence?

Back

The nth term of a geometric sequence can be calculated using the formula: g_n = g_1 * r^(n-1), where g_1 is the first term and r is the common ratio.

Front

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

Back

The sum 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 of the first n terms of a geometric series can be calculated using the formula: S_n = g_1 * (1 - r^n) / (1 - r), for r ≠ 1.

Front

What is the common difference in an arithmetic sequence?

Back

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

Front

What is the common ratio in a geometric sequence?

Back

The common ratio is the fixed number that each term in a geometric sequence is multiplied by to get the next term.

Front

Evaluate the sum of the geometric series: 4, -8, 16, -32..., n = 7.

Back

The sum is 518.

Front

Find the sum of the arithmetic series: 2 + (-2) + (-6) + (-10)..., S_10.

Back

The sum is -160.