Sequences Review

A theatre has 35 seats in the first row. Each row has four more seats than the row before it. Which expression represents the number of seats in the nth row?

• $35+\left(n+4\right)$

• $35+\left(4n\right)$

• $35+\left(n+1\right)\left(4\right)$

• $35+\left(n-1\right)\left(4\right)$

 At her job, Pat earns $25,000 the first year and receives a raise of $1000 each year. The explicit formula for the nth term of this sequence is  $a_n=25,000+\left(n-1\right)1000$ .  Which rule best represents the equivalent recursive formula?

•  $a_n=24,000+1000n$  

•  $a_n=25,000+1000n$  

•  $a_1=25,000,\ \ a_n=a_{n-1}+1000$  

•  $a_1=25,000,\ \ a_n=a_{n+1}+1000$  

The population of Jamesburg for the years 2010-2013, respectively, was reported as follows:

250,000 | 250,937 | 251,878 | 252,822

How can this sequence be recursively modeled?

• $j_n=250,000\left(1.00375\right)^{n-1}$

• $j_n=250,000+937^{\left(n-1\right)}$

• $j_1=250,000$
  $j_n=1.00375j_{n-1}$
  

• $j_1=250,000$
  $j_n=j_{n-1}+937$
  

In 2010, the population of New York State was approximately 19,378,000 with an annual growth rate of 1.5%. Assuming the growth rate is maintained for a large number of years, which equation can be used to predict the population of New York State t years after 2010?

• $P_t=19,378,000\left(1.5\right)^t$

• $P_0=19,378,000$
  $P_t=19,378,000+1.015P_{t-1}$
  

• $P_t=19,378,000\left(1.015\right)^{t-1}$

• $P_0=19,378,000$
  $P_t=1.015P_{t-1}$
  

The average depreciation rate of a new boat is approximately 8% per year. If a new boat is purchased at a price of $75,000, which model is a recursive formula representing the value of the boat n years after it was purchased?

• $a_n=75,000\left(0.08\right)^n$

• $a_0=75,000$
  $a_n=\left(0.92\right)^n$
  

• $a_n=75,000\left(1.08\right)^n$

• $a_0=75,000$
  $a_n=0.92\left(a_{n-1}\right)$
  

Savannah just got contact lenses. Her doctor said she can wear them 2 hours the first day, and can then increase the length of time by 30 minutes each day. If this pattern continues, which formula would not be appropriate to determine the length of time, in either minutes or hours, she could wear her contact lenses on the nth day?

• $a_1=120$
  $a_n=a_{n-1}+30$
  

• $a_n=90+30n$

• $a_1=2$
  $a_n=a_{n-1}+0.5$
  

• $a_n=2.5+0.5n$

The Rickerts decided to set up an account for their daughter to pay for her college education. The day their daughter was born, they deposited $1000 in an account that pays 1.8% compounded annually. Beginning with her first birthday, they deposit an additional $750 into the account on each of her birthdays. Which expression correctly represents the amount of money in the account n years after their daughter was born?

• $a_n=1000\left(1.018\right)^n+750$

• $a_n=1000\left(1.018\right)^n+750n$

• $a_0=1000$
  $a_n=a_{n-1}\left(1.018\right)+750$
  

• $a_0=1000$
  $a_n=a_{n-1}\left(1.018\right)+750n$
  

After Roger's surgery, his doctor administered pain medication in amounts (in milligrams) over four days as shown in the table above.

How can this sequence be best modeled recursively?

• $m_1=2000$
  $m_n=m_{n-1}-320$
  

• $m_n=2000\left(0.84\right)^{n-1}$

• $m_1=2000$
  $m_n=\left(0.84\right)m_{n-1}$
  

• $m_n=2000\left(0.84\right)^{n+1}$

Which situation could be modeled using a geometric sequence?

• A cell phone company charges $30.00 per month for 2 gigabytes of data and $12.50 for each additional gigabyte of data.

• The temperature in your car is 79^o. You lower the temperature of your air conditioning by 2^o every 3 minutes in order to find a comfortable temperature.

• David's parents have set a limit of 50 minutes per week that he may play online games during the school year. However, they will increase his time by 5% per week for the next ten weeks.

• Sarah has $100.00 in her piggy bank and saves an additional $15.00 each week.

The formula below can be used to model which scenario?

 $a_1=3000$  
 $a_n=0.80a_{n-1}$  

• The first row of a stadium has 3000 seats, and each row thereafter has 80 more seats than the row in front of it.

• The last row of a stadium has 3000 seats, and each row before it has 80 fewer seats than the row behind it.

• A bank account starts with a deposit of $3000, and each year it grows by 80%.

• The initial value of a speciality toy is $3000 and its value each of the following years is 20% less.