Quiz about Arithmetic and Geometric Sequences Review

Question 1

What is the common difference or common ratio of the given sequence?

23, 223, 423, 643, 843,...

Accepted Answer

d = 200

Answer

r = 200

Answer

r = 9.6

Answer

d = 9.6

Question 2

What is the common difference or common ratio of the given sequence?

-1, 3, -9, 26, -81,...

Accepted Answer

r = -3

Answer

d = 4

Answer

r = 3

Answer

d = -3

Question 3

What is the common difference or common ratio of the given sequence?

-39, -41, -43, -45, -47,...

Accepted Answer

d = -2

Answer

r = -2

Answer

d = 2

Answer

r = 2

Question 4

What is the common difference or common ratio of the given sequence?

243, 81, 27, 9, 3,...

Accepted Answer

$$r=\frac{1}{3}$$

Answer

$$r=-3$$

Answer

$$d=-\frac{1}{3}$$

Answer

$$d=3$$

Question 5

Which of the following are true about an arithmetic sequence?

Accepted Answer

The same amount is added to go from one term to to the next term.

Accepted Answer

The same amount is subtracted to go from one term to the next term.

Answer

To go from one term to the next term, terms are multiplied by the same amount.

Answer

To go from one term to the next term, terms are divided by the same amount.

Question 6

Which of the following are true about a geometric sequence?

Accepted Answer

To go from one term to the next term, terms are multiplied by the same amount.

Accepted Answer

To go from one term to the next term, terms are divided by the same amount.

Answer

The same amount is added to go from one term to the next term.

Answer

The same amount is subtracted to go from one term to the next term.

Question 7

To find the common difference of an arithmetic sequence you can ....

Accepted Answer

Take the second term and subtract the first term.

Accepted Answer

Take the third term and subtract the second term.

Answer

Take the second term and subtract the 4th term.

Answer

Take the second term and divide it by the first term.

Question 8

To find the common ratio of a geometric sequence you can ....

Accepted Answer

Take the second term and divide it by the first term.

Accepted Answer

Take the third term and divide it by the second term.

Answer

Take the second term and divide it by the 4th term.

Answer

Take the second term and subtract the first term.

Question 9

If $$a_1=38,\ and\ d=30$$ , what is the explicit formula?

Accepted Answer

$$a_n=38+30\left(n-1\right)$$

Answer

$$a_n=38\left(30\right)^{\left(n-1\right)}$$

Answer

$$a_n=30\left(38\right)^{\left(n-1\right)}$$

Answer

$$a_n=30+38\left(n-1\right)$$

Question 10

If $$a_1=-4,\ and\ r=-3$$ , what is the explicit formula?

Accepted Answer

$$a_n=-4\left(-3\right)^{\left(n-1\right)}$$

Answer

$$a_n=-3\left(-4\right)^{\left(n-1\right)}$$

Answer

$$a_n=-4+-3\left(n-1\right)$$

Answer

$$a_n=-3+-4\left(n-1\right)$$

Question 11

If $$a_1=243,\ and\ r=\frac{1}{3}$$ , what is the explicit formula?

Accepted Answer

$$a_n=243\left(\frac{1}{3}\right)^{\left(n-1\right)}$$

Answer

$$a_n=\frac{1}{3}\left(243\right)^{\left(n-1\right)}$$

Answer

$$a_n=\frac{1}{3}+243\left(n-1\right)$$

Answer

$$a_n=243+\frac{1}{3}\left(n-1\right)$$

Question 12

Given the explicit formula $$a_n=3+-4\left(n-1\right)$$ .

Find $$a_{26}$$

Accepted Answer

-97

Answer

103

Answer

668

Answer

-101

Question 13

Given the explicit formula $$a_n=38+30\left(n-1\right)$$ .

Find $$a_{22}$$

Accepted Answer

668

Answer

698

Answer

-97

Answer

25080

Question 14

Given the explicit formula $$a_n=-40+10\left(n-1\right)$$ .

Find $$a_{23}$$

Accepted Answer

180

Answer

-260

Answer

-870

Answer

190

Question 15

Given the explicit formula $$a_n=-18+-5\left(n-1\right)$$ .

Find $$a_{35}$$

Accepted Answer

-188

Answer

-152

Answer

190

Answer

180

Question 16

Given the explicit formula $$a_n=-4\left(\frac{1}{2}\right)^{\left(n-1\right)}$$ .

Find $$a_{12}$$

Accepted Answer

-0.00195

Answer

-8192

Answer

-3072

Answer

-0.00097

Question 17

Given the explicit formula $$a_n=-3\left(-2\right)^{\left(n-1\right)}$$ .

Find $$a_{11}$$

Accepted Answer

-3072

Answer

6144

Answer

-0.00097

Answer

-0.00195

Question 18

What is the explicit formula for the given sequence?

$$-40,\ -30,\ -20,\ -10,\ ...$$

Accepted Answer

$$a_n=-40+10\left(n-1\right)$$

Answer

$$a_n=-40-10\left(n-1\right)$$

Answer

$$a_n=10+-40\left(n-1\right)$$

Answer

$$a_n=-40\left(10\right)^{\left(n-1\right)}$$

Question 19

What is the explicit formula for the given sequence?

$$-18,\ -23,\ -28,\ -33,\ ...$$

Accepted Answer

$$a_n=-18-5\left(n-1\right)$$

Answer

$$a_n=-18+5\left(n-1\right)$$

Answer

$$a_n=5+-18\left(n-1\right)$$

Answer

$$a_n=-18\left(-5\right)^{\left(n-1\right)}$$

Question 20

What is the explicit formula for the given sequence?

$$-4,\ -2,\ -1,\ -\frac{1}{2},\ ...$$

Accepted Answer

$$a_n=-4\left(\frac{1}{2}\right)^{\left(n-1\right)}$$

Answer

$$a_n=-4\left(\frac{1}{2}\right)\left(n-1\right)$$

Answer

$$a_n=-4+2\left(n-1\right)$$

Answer

$$a_n=-4\left(2\right)^{\left(n-1\right)}$$

Question 21

What is the explicit formula for the given sequence?

$$-3,\ 6,\ -12,\ 24,\ ...$$

Accepted Answer

$$a_n=-3\left(-2\right)^{\left(n-1\right)}$$

Answer

$$a_n=-3+-2\left(n-1\right)$$

Answer

$$a_n=-3\left(2\right)^{\left(n-1\right)}$$

Answer

$$a_n=-2\left(-3\right)^{\left(n-1\right)}$$

Arithmetic and Geometric Sequences Review

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