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

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.

Front

What is the common difference in the sequence 10, 15, 20, 25?

Back

The common difference is d = 5.

Front

Write a recursive formula for the sequence 2, 4, 6, 8, ...

Back

a(1) = 2; a(n) = a(n-1) + 2.

Front

What is the difference between two numbers in an arithmetic sequence called?

Back

The difference is called the common difference.

Front

Find the next two terms of the sequence 5, 10, 15, 20.

Back

The next two terms are 25 and 30.

Front

If the common difference is -4, what is the 3rd term if the first term is 12?

Back

The 3rd term is 12 + 2(-4) = 4.

Front

What is the 10th term of the sequence 3, 7, 11, 15?

Back

The 10th term is 3 + 9(4) = 39.