Unit 1: Sequences Review

Four arithmetic sequences are shown.

How do their common differences compare? Place them in order of the common difference from LEAST to GREATEST

Four geometric sequences are given.

How do their ratios compare? Place them in order from LEAST common ratio to GREATEST common ratio.

Write an equation that models the sequence shown in the table. Simplify.

The value of a classic car increases every year. The relationship between the number of years, n, and the value of the car V(n), in dollars is shown in the table.

Which of these functions could represent the nth term of the pattern shown. Choose yes or no for each.

$$V\left(n\right)=29250\left(1.17\right)^n$$ ​ ​ (a)  

$$V\left(n\right)=29250\left(1.17\right)^{\left(n-1\right)}$$ ​ (b)  

$$V\left(n\right)=25000\left(1.17\right)^n$$ ​ (c)  

$$V\left(n\right)=25000\left(1.17\right)^{\left(n-1\right)}$$ ​ (d)  

Consider this function in recursive form:

$$a_1=39;\ a_n=a_{\left(n-1\right)}+4$$

What is the 4th term?

(a)  

Consider this function in recursive form:

$$a_1=39;\ a_n=a_{\left(n-1\right)}+4$$

What is the 22nd term?

(a)  

Consider this function in recursive form:

$$a_1=39;\ a_n=a_{\left(n-1\right)}+4$$

What is the 52nd term?

(a)  

The figure below shows the number of dots in each of the first three terms of a pattern.

Determine the sequence for this pattern. How many dots would there be in the 10th term?

(a)  

A sequence is define recursively by the formula below:

$$a_1=64$$

$$a_n=\frac{1}{4}\cdot a_{\left(n-1\right)}$$

What is the $$a_4$$ term of the sequence?

Use decimal form if necessary.

A sequence is define recursively by the formula below:

$$a_1=64$$

$$a_n=\frac{1}{4}\cdot a_{\left(n-1\right)}$$

What is the $$a_7$$ term of the sequence?

Use decimal form if necessary.