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) is found by subtracting any term from the subsequent term: d = a(n) - a(n-1).

Front

Given the sequence 29, 21, 13, 5, what is the common difference?

Back

d = -8.

Front

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

Back

Yes, it is an arithmetic sequence.

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

Select the explicit rule for the sequence: 6, 11, 16, 21,...

Back

a(n) = 6 + 5(n - 1).

Front

Given the sequence 1, 201, 401, 601, what is the common difference?

Back

d = 200.

Front

Select the explicit rule for the sequence: 14, 11, 8, 5,...

Back

a(n) = 14 + (n - 1)(-3).

Front

What does it mean for a sequence to be arithmetic?

Back

It means that the difference between any two consecutive terms is always the same.

Front

If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?

Back

a(10) = 5 + (10 - 1)3 = 32.