Arithmetic Sequences

Front

What is an arithmetic sequence?

Back

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

Front

Define the common difference (d) in an arithmetic sequence.

Back

The common difference (d) is the fixed amount that each term in an arithmetic sequence increases or decreases by.

Front

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

Back

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

Front

Given the first term a_1 = 3 and common difference d = 2, what is the 5th term?

Back

The 5th term is a_5 = 3 + (5 - 1) * 2 = 3 + 8 = 11.

Front

How do you find the first four terms of an arithmetic sequence given a_1 and d?

Back

To find the first four terms, start with a_1 and add d successively: a_1, a_1 + d, a_1 + 2d, a_1 + 3d.

Front

What is a recursive formula for an arithmetic sequence?

Back

A recursive formula defines each term based on the previous term: a_n = a_(n-1) + d, with a_1 defined.

Front

If a_1 = -5 and d = 3, list the first four terms of the sequence.

Back

The first four terms are: -5, -2, 1, 4.

Front

What is the explicit formula for the sequence defined by a_n = 22 - 5(n-1)?

Back

The explicit formula is a_n = 22 - 5(n-1), which can be simplified to a_n = 27 - 5n.

Front

How do you determine the common difference from a sequence?

Back

The common difference can be found by subtracting any term from the subsequent term: d = a_(n+1) - a_n.

Front

Given the sequence -18, -23, -28, -33, what is the common difference?

Back

The common difference is d = -23 - (-18) = -5.