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

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

Back

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

Front

Given the sequence 7, 27, 47, 67, what is the common difference?

Back

The common difference is 20.

Front

What are the next three terms in the arithmetic sequence: -33, -24, -15, -6?

Back

The next three terms are 3, 12, 21.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 5th term?

Back

The 5th term is 5 + 4*3 = 17.

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 can you determine if a sequence is arithmetic?

Back

A sequence is arithmetic if the difference between consecutive terms is the same for all pairs of terms.

Front

What is the common difference in the sequence: -34, -29, -24, -19?

Back

The common difference is 5.

Front

If an arithmetic sequence has a common difference of -2, what is the next term after 10?

Back

The next term is 10 - 2 = 8.

Front

What is the 10th term of the arithmetic sequence starting with 2 and having a common difference of 4?

Back

The 10th term is 2 + (10-1)*4 = 38.