Arithmetic and Geometric Sequences

Arithmetic

100

Is this sequence arithmetic? If so, what is the common difference? If not, why is it not arithmetic? 1.5, 4, 6.5,...

Yes. What is d = 2.5?

200

Is this sequence arithmetic? If so, what is the common difference? If not, why is it not arithmetic? 4, -5, -14, -25,...

No. This is not arithmetic, because you are not adding the same amount each time.

300

The 7th term in the arithmetic sequence: 3, 7, 11, 15...?

What is 27?

400

The value of the 1st term when the 23rd term is 36 and the common difference is 2.

What is -8?

500

This is the common difference when the first term is 25 and the 76th term is 175.

What is 2?

Geometric

100

Is the following sequence geometric? If so, what is the common ratio? 54, 18, 6, 2, ...

Yes. What is r = 1/3?

200

List the first three terms in the sequence, a_n = 2(3)^(n-1)

What is 2, 6, 18?

300

This is the common ratio when the 1st term is 2 and the 3rd term is 72.

What is 6?

400

This is the value of the first term when the 5th term is 512 and the common ratio is 4.

What is 2?

500

This is the the common ratio when the 2nd term is 6 and the 4th term is 54.

Double Points!!

What is 3?

Formula

100

The formula for a_n from the arithmetic sequence: 2, 6, 10, 14, 18.......

What is a_n = 2 + 4(n - 1) or a_n = 4n-2?

200

The formula for a_n from the arithmetic sequence: -1, 2, 5, 8, 11

What is a_n = -1 + 3(n - 1) or a_n = 3n - 4?

300

What is the equation for a_n the following geometric sequence? 1.5, -6, 24 ...

What is a_n = 1.5(-4)^n?

400

In an arithmetic sequence, the 4th term is 18 and the common difference is 7. What is the equation for the a_n?

What is a_n = -3 + 7(n - 1) ir a_n = 7n - 10

500

In a geometric sequence, the 5th term is 81 and the common ratio is 1/3. Write the equation for a_n.

Double Points!!!

What is a_n = 6561(1/3)^(n-1)