3.12 Arithmetic Sequence Practice

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 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

How do you find the common difference in an arithmetic sequence?

Back

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

Front

If the first term of an arithmetic sequence is 5 and the common difference is 4, what is the 10th term?

Back

The 10th term is 5 + (10-1) * 4 = 5 + 36 = 41.

Front

What is the 100th term of the arithmetic sequence 5, 9, 13, 17,...?

Back

The 100th term is 5 + (100-1) * 4 = 5 + 396 = 401.

Front

If the first term of an arithmetic sequence is 2 and the 18th term is 87, how do you find the common difference?

Back

Use the formula: a_n = a_1 + (n-1)d. Here, 87 = 2 + (18-1)d. Solving gives d = 5.

Front

What is a recursive formula in the context of sequences?

Back

A recursive formula defines each term of a sequence using the previous term(s). For example, a_n = a_(n-1) - 8.

Front

What is an explicit formula in the context of sequences?

Back

An explicit formula allows you to find the nth term directly without needing previous terms. For example, a_n = 5n + 4.

Front

How do you find the first term of an arithmetic sequence if you know the 14th term and the common difference?

Back

Use the formula: a_14 = a_1 + (14-1)d. Rearranging gives a_1 = a_14 - (14-1)d.

Front

What is the 64th term of the sequence defined by a_n = 5n + 4?

Back

The 64th term is a_64 = 5(64) + 4 = 320 + 4 = 324.