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

Front

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

Back

The nth term (a_n) 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

What is the explicit formula for the arithmetic sequence: 5, 12, 19, 26...?

Back

The explicit formula is a_n = 5 + 7(n - 1).

Front

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

Back

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

Front

Identify the common difference in the sequence: 10, 20, 30, 40...

Back

The common difference is 10.

Front

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

Back

Yes, the common difference is -8.

Front

Which equation represents the sequence: 6, 11, 16, 21...?

Back

The equation is a_n = 6 + 5(n - 1).

Front

Find the 25th term of the sequence if a_1 = 5 and d = 0.5.

Back

a_25 = 5 + 0.5(25 - 1) = 17.

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.