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

What is the common difference in an arithmetic sequence?

Back

The common difference is the fixed amount added to each term to get the next term in the sequence.

Front

How do you find the nth term of an arithmetic sequence?

Back

The nth term can be found 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 sequence: 5, 12, 19, 26, what is the common difference?

Back

The common difference is 7.

Front

Find a_20 in the arithmetic sequence: 5, 12, 19, 26...

Back

a_20 = 5 + (20-1)7 = 138.

Front

Is the sequence 17, 9, 1, -7 arithmetic?

Back

Yes, the common difference is -8.

Front

Write the explicit equation for the sequence: 25, 21, 17, 13...

Back

a_n = 25 - 4(n-1).

Front

What are the next two terms of the sequence 4, 7, 10, 13?

Back

The next two terms are 16 and 19.

Front

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

Back

The 10th term is 10 + (10-1)5 = 55.

Front

What is the formula for the sum of the first n terms of an arithmetic sequence?

Back

The sum S_n = n/2 * (a_1 + a_n), where a_n is the nth term.