Arithmetic Sequences and Explicit Formula

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

What is the common difference in an arithmetic sequence?

Back

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

Front

How do you find the next term in an arithmetic sequence?

Back

To find the next term, add the common difference to the last term.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula is given by a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

Given the sequence 3, 7, 11, 15, what are the next three terms?

Back

The next three terms are 19, 23, 27.

Front

Create the explicit formula for the sequence 2, 8, 14.

Back

The explicit formula is a_n = 6n - 4.

Front

What is the explicit formula for the sequence 2, 9, 16, 23?

Back

The explicit formula is a_n = 7n - 5.

Front

Identify the common difference in the sequence -6, -3, 0, 3, 6.

Back

The common difference is d = 3.

Front

Find the 22nd term of the sequence 5, 8, 11.

Back

The 22nd term is 68.

Front

What is the first term of an arithmetic sequence?

Back

The first term (a_1) is the initial term of the sequence from which all other terms are derived.