Q: A savings account earns 5% interest compounded annually. If $$125 is $$deposited and left untouched for $$9$$ years, what is the amount in the account after $$9$$ years?

$$125 \times 1.05^9$ = 193.92$$

Q: Nicole deposits $$100$$ monthly into a bank account earning $$0.5\%$$ interest compounded monthly. What is the formula for the accumulated amount after $$72$$ deposits?

$$S_{72} = 100 \times \frac{1 - (1.005$$)^{72}$$}{1 - 1.005}$$

Q: What is the formula for the sum of the first $$n$$ terms of a geometric sequence with first term $$a$$ and common ratio $$r$$?

$$S_n = a \times \frac{1 - r^n}{1 - r}$$

Question 1

Which of the following is the correct formula for the nth term of an arithmetic sequence with first term $$a$$ and common difference $$d$$?

Accepted Answer

$$a_n = a + d(n-1)$$

Question 2

A savings account earns 5% interest compounded annually. If $$125 is $$deposited and left untouched for $$9$$ years, what is the amount in the account after $$9$$ years?

Accepted Answer

$$125 	imes 1.05^9$ = 193.92$$

Question 3

Which of the following sequences is geometric?

Accepted Answer

$$3, 6, 12, 24, 48$$

Question 4

A grocery store stocks $$90$$ cans of soup and sells $$3$$ cans each day. What is the inventory level on day $$n$$ after restocking?

Accepted Answer

$$a_n = 87 - 3(n-1)$$

Question 5

What is the sum of the first $$n$$ terms of an arithmetic sequence with first term $$a$$ and last term $$a_n$$?

Accepted Answer

$$S_n = \frac{n}{2}(a + a_n)$$

Question 6

Nicole deposits $$100$$ monthly into a bank account earning $$0.5\%$$ interest compounded monthly. What is the formula for the accumulated amount after $$72$$ deposits?

Accepted Answer

$$S_{72} = 100 	imes \frac{1 - (1.005$$)^{72}$$}{1 - 1.005}$$

Question 7

Which of the following infinite geometric series converges?

Accepted Answer

$$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ...$$

Question 8

A business expects daily revenue to increase by $$1000$$ each day for $$31$$ days, starting at $$12,000 on $$day 1. What is the total projected revenue for the $$31$$ days?

Accepted Answer

$$837,000$$

Question 9

What is the formula for the sum of the first $$n$$ terms of a geometric sequence with first term $$a$$ and common ratio $$r$$?

Accepted Answer

$$S_n = a 	imes \frac{1 - r^n}{1 - r}$$

Question 10

A government gives a $$1,000$$ tax rebate, and each recipient spends $$80\% of it$$, which is then spent again at $$80\%$$, and so on. What is the total effect of the rebate on the economy?

Accepted Answer

$$5,000$$

Question 11

What is the sum of the infinite geometric series $$54 + 36 + 24 + ...$$?

Accepted Answer

$$135$$

Question 12

Which of the following is a recursive formula for the Fibonacci sequence?

Accepted Answer

$$F_n = F_{n-1} + F_{n-2}$$, with $$F_1 = 1$, F_2$ = 1$$

Question 13

If the first term of a geometric sequence is $$2$$ and the common ratio is $$-5$$, what is the 4th term?

Accepted Answer

$$-250$$

Question 14

A perpetuity pays $$100,000$$ per year, starting now, with funds invested at $$2\%$$ compounded annually. What is the minimum investment required to fund this perpetuity?

Accepted Answer

$$5,100,000$$

Question 15

Which property of summation notation is correct for sequences $$a_i$$ and $$b_i$$ and constant $$c$$?

Accepted Answer

$$\sum_{i=1}^n (a_i + b_i) = \sum_{i=1}^n a_i + \sum_{i=1}^n b_i$$

Question 16

Given the sequence $$a_n = 2n - 1$$, what is the 100th term?

Accepted Answer

$$199$$

Question 17

Which of the following is NOT a way to define a sequence?

Accepted Answer

By specifying only the first term

Question 18

If an arithmetic sequence has $$a_1 = 13$ and d = -6$, what is the 6th term?

Accepted Answer

$$-17$$

Question 19

What is the formula for the nth term of a geometric sequence with first term $$a$$ and common ratio $$r$$?

Accepted Answer

$$a_n = a r$$^{n-1}$$

QMS110 Lecture 10

Guida di studio - Domande di pratica

Study guide - Flashcard