Unit 8: Sequences and Series Review

Select two numbers that could be the sum of the first nine terms of a geometric series with the given first and ninth terms.

$$a_1=-3$$  and $$a_9=-768$$  

Given the first and the last terms of an eight-term geometric series with a negative common ratio, what is the sum of all the terms?

$$3-.\ .\ .\ -6561$$  

Amy ran 3 miles to prepare for her marathon on the first day of practice. Each day she ran 2 more miles than the previous day. She wrote a formula to see how many miles she would run over the next few days of practice. The formula is shown: $$a_1=3,\ a_n=a_{\left(n-1\right)}+2$$  

Which formula is equivalent to the one Amy wrote?

Greg posted a tiktok video that received 400 hits the first day.  Each day the number of hits doubled.  He wrote a formula to see how many hits his video would receive in the next few days.  The formula is shown below.

$$a_n=400\left(2\right)^{\left(n-1\right)}$$  

Which formula is equivalent to the one Greg wrote?

What is the rule for the nth term of the sequence given below?

$$14,\ 6,\ -2,\ -10,\ .\ .\ .\$$  

What are the second, third, and fourth terms of the sequence defined by the formula below?

$$a_1=-7\ ;\ a_n=a_{\left(n-1\right)}+200$$  

What is the sum of the infinite geometric series?

$$-6-2-\frac{2}{3}-\frac{2}{9}.\ .\ .\$$  

Harley wants to calculate the sum of the first six terms of the geometric sequence $$-2,\ -6,\ -18,\ -54,\ .\ .\ .\$$   Which of the following formulas will she need to use?

You and your friend are going to a private concert. The first row in the venue seats 8. Each row after has 3 more in it then the row before. If there are 10 rows in this venue, how many seats are in the venue?

Maribell wrote an arithmetic sequence where $$a_1=24$$  and the common difference is $$4$$  .

What is a rule for the nth term of this sequence?