Arithmetic and Geometric Sequences

Front

What is the definition of an arithmetic sequence?

Back

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

Front

What is the definition of a geometric sequence?

Back

A geometric sequence is a sequence of numbers in which 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 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

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

Back

The nth term of a geometric sequence can be found using the formula: u_n = u_1 * r^(n-1), where u_1 is the first term and r is the common ratio.

Front

What is the common difference in an arithmetic sequence?

Back

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

Front

What is the common ratio in a geometric sequence?

Back

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

Front

If the first term of an arithmetic sequence is 5 and the common difference is 2, what is the 10th term?

Back

The 10th term is 23.

Front

If the first term of a geometric sequence is 3 and the common ratio is 4, what is the 5th term?

Back

The 5th term is 192.

Front

What is the sum of the first n terms of an arithmetic sequence?

Back

The sum of the first n terms of an arithmetic sequence 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 sum of the first n terms of a geometric sequence?

Back

The sum of the first n terms of a geometric sequence can be calculated using the formula: S_n = u_1 * (1 - r^n) / (1 - r), for r ≠ 1.