Question

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2. –4, 8, –16, 32, . . .
A. arithmetic, 64, 128, 256
B. geometric, –64, 128, –256
C. geometric, –48, 64, –80
D. The sequence is neither geometric nor arithmetic.

3. 81, 27, 9, 3, . . .
A. arithmetic, 0, –3, –6
B. geometric, 0, –3, –6
C. geometric, 1,
D. The sequence is neither geometric nor arithmetic.

4. What are the first four terms of an arithmetic sequence if the common difference is 1.5 and the first term is 15?
A. 15, 30, 45, 60
B. 15, 16.5, 18, 19.5
C. 15, 22.5, 33.75, 50.625
D. none of the above

5. What are the first four terms of a geometric sequence if the common ratio is 10 and the first term is 4.5?
A. 4.5, .45, .045, .0045
B. 4.5, 9.0, 13.5, 18.0
C. 4.5, 14.5, 24.5, 34.5
D. none of the above

Answer 1

Answer:

2. B

3. C

4. B

5. D

Step-by-step explanation:

2) The sequence is multiplying by -2 each time. This means that it is geometric.

The next two terms would be:

$32*-2=-64\\-64*-2=128\\128*-2=-256$

This means that the answer is B

3) The sequence is being multiplied by $\frac{1}{3}$ each time. This means that it is geometric.

The next 3 terms would be:

$3*\frac{1}{3} =1 \\\\1*\frac{1}{3} =\frac{1}{3} \\\\\frac{1}{3} *\frac{1}{3} =\frac{1}{9}$

I am assuming that the answer is C and that you were unable to type the fractions.

4) We know that the common difference is 1.5, so that is the coefficient of our variable and the starting value is 15. This means that we can write an equation as follows

$f(x)=1.5(x-1)+15$

Now we can find the first 4 terms

$f(1)=15.0\\f(2)=16.5\\f(3)=18.0\\f(4)=19.5$

This would mean that the answer is B

5) We know that this is a geometric series, we know the common ratio, and we know the first term. This means we can write the equation as follows

$f(x)=4.5(10)^{x-1}$

Now we can find the first 4 terms

$f(1)=4.5\\f(2)=45\\f(3)=450\\f(4)=4500$

Unless you meant that the ratio was $\frac{1}{10}$, the answer is D, none of the above