Sequences — Quiz 4

Questions in this quiz (6)

1. What is the 10th term in the geometric sequence $$16, -8, 4, -2,....$$?

   • $$\frac{-1}{32}$$
   • $$\frac{-1}{512}$$
   • $$\frac{1}{512}$$
   • $$\frac{-1}{16}$$

2. In the arithmetic sequence below, how many terms are there between $$-12$$ and $$-40$$, exclusive of $$-12$$ and $$-40$$?$$-4, -8, -12, -16, -20, \dots, -40$$

   • $$6$$
   • $$7$$
   • $$8$$
   • $$10$$

3. Emma borrowed $$30000$$ from a bank to purchase a home appliance. The bank charges her $$0.6\%$$ interest per month on any unpaid balance, and she will pay $$400$$ toward the balance each month. If Emma's balance each month after making a $$400$$ payment is defined by the recurrence relation:$$a_0=30000$$$$a_{n+1}=1.006a_n-400, \quad \text{for } n \geq 0$$What is Emma's balance after she makes the fourth payment?

   • $$29,650$$
   • $$29,112$$
   • $$29,336$$
   • $$29,780$$

4. Which term of the arithmetic progression: $$3, 15, 27, 39, \ldots$$ will be 132 more than its $$54^{th}$$ term?

   • $$64^{th}$$
   • $$65^{th}$$
   • $$63^{th}$$
   • $$62^{th}$$

5. For what value of $$n$$ are the $$n^{th}$$ terms of two arithmetic progressions $$63, 65, 67, \ldots$$ and $$3, 10, 17, \ldots$$ equal?

   • 4
   • 7
   • 13
   • 5

6. Find the $$31^{st}$$ term of an arithmetic progression whose $$11^{th}$$ term is $$38$$ and $$16^{th}$$ term is $$73$$.

   • 178
   • 210
   • 70
   • 32