Arithmetic Sequence (Recursive and Explicit)

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 in an arithmetic sequence.

Back

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

Front

How do you find the common difference in a sequence?

Back

Subtract the first term from the second term (d = a2 - a1).

Front

Is the sequence 1, 3, 5, 7, ... arithmetic?

Back

Yes, the common difference is 2.

Front

What is the explicit formula for an arithmetic sequence?

Back

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

Front

What is the recursive formula for an arithmetic sequence?

Back

The recursive formula is a_n = a_(n-1) + d, where d is the common difference.

Front

Given the sequence 4, 10, 16, ..., find the common difference.

Back

The common difference is 6.

Front

Determine if the sequence 2, 4, 8, 16, ... is arithmetic.

Back

No, the common difference is not constant.

Front

Find the next three terms in the sequence: 5, 10, 15, ...

Back

The next three terms are 20, 25, 30.

Front

What is the first term of the sequence defined by a_n = 3 + 5(n-1)?

Back

The first term is 3.