Geometric and Arithmetic Sequence

What are the next three terms in the arithmetic sequence below:

1, 8, 15, , ,

Answer explanation

To Find the common difference subtract 8-1 and you get the common difference of 7, so you add 7 to each term to get the next and you get 15+7=22, 22+7=29, 29+7=36 so the next 3 in the sequence are:

22, 29, and 36

Match the following geometric sequences with their common ratios:

• 2

• 144, 36, 9, 2.25, . . .

• 4

• 2, 8, 32, 128, . . .

• 0.25

• 3, 6, 12, 24, 48, . . .

The town of Ardmore is studying its decreasing population. In the 1st year of the study, the population was 3,045 people. In the 5th year of the study, the population had decreased by a factor of 0.87. If the population of Ardmore continues to decrease in this way, what will be the explicit formula for the geometric sequence that represents Ardmore's population for the years during the study? The first term = ​ ​ (a)   The common ratio = ​ (b)   The explicit formula = ​ ​ (c)  

• 3045

• 0.87

• 1

• 5

What is the difference between an arithmetic sequence and a geometric sequence?

• One is the sum of the numbers and one is just a list of numbers.

• One has a common difference and one has a common ratio.

• One you can write an nth term and one you cannot.

• None of these are correct.

What do we call this sequence: 6,18,54,162,…

• Arithmetic Sequence

• Geometric Sequence

• Fibonacci Sequence

• Triangular Sequence

What do we call this sequence: 1, 31, 61, 91,...

• Arithmetic Sequence

• Geometric Sequence

• Square Number Sequence

• Cube Number Sequence

256, 128, 64, 32, ...

What's next?

• 24

• 18

• 16

• 8

Given the sequence 2, 8, 14, 20, 26, ... What is the common difference?

• 2

• 4

• 6

• 8