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

Write the recursive formula for the arithmetic sequence: 6, 17, 28, 39, 50.

Back

a_n = a_{n-1} + 11, a_1 = 6.

Front

Find the common difference for the sequence: -34, -29, -24, -19.

Back

d = 5.

Front

Is the sequence 37, 31, 25, 19 arithmetic?

Back

Yes.

Front

Find a_20 in the arithmetic sequence: 5, 12, 19, 26... (Hint: Find explicit formula first)

Back

a_20 = 138.

Front

What is the explicit formula for an arithmetic sequence?

Back

The explicit formula is a_n = a_1 + (n-1)d.

Front

If a_1 = 5 and d = 0.5, what is the 25th term of the sequence?

Back

a_{25} = 17.

Front

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

Back

Use the formula a_n = a_1 + (n-1)d.

Front

What does it mean for a sequence to be arithmetic?

Back

It means that the sequence has a constant difference between consecutive terms.