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1.    classify as arithmetic, geometric, or neither. Finally find an explicit formula (rule for the nth term) for each.  Designate the first term with n = 1.

asked Jan 29, 2015 in PRECALCULUS by anonymous

5 Answers

0 votes

Step 1:

The series is image.

The arithmetic series have the common difference.

The geometric series have the common ratio.

The above series is in the form  of arithmetic series.

Arithmetic series is image.

Where image is first term

            image is common difference.

Common difference image.

Where image is image term .

            image is image term .

image term in arithmetic series image.

Step 2:

Now compare the above equation with arithmetic series.

The first term in the given series is image.

Common difference image.

image

image term in arithmetic series image.

image

image.

Solution :

The series is in the form  of arithmetic series.

answered Jan 29, 2015 by yamin_math Mentor
0 votes

(b)

Step 1:

The series is image.

The arithmetic series have the common difference.

The geometric series have the common ratio.

The above series is in the form  of arithmetic series.

Arithmetic series is image.

Where image is first term

            image is common difference.

Common difference image.

Where image is image term .

            image is image term .

image term in arithmetic series image.

Step 2:

Now compare the above equation with arithmetic series.

The first term in the given series is image.

Common difference .

image

term in arithmetic series .

image

image.

Solution :

The series is in the form  of arithmetic series.

 

answered Jan 30, 2015 by yamin_math Mentor
edited Jan 30, 2015 by yamin_math
0 votes

(c)

Step 1:

The series is .

The above series have the common constant ratio.

So above series is in the form  of geometric series.

geometric series :

.

Where is first term

            is common ration.

Common ration .

Where is term .

            is term .

term in geometric series .

Step 2:

Now compare the above equation with geometric series.

The first term in the given series is .

Common ratio .

term in geometric series .

image.

Solution :

The series is in the form  of geometric series.

answered Jan 30, 2015 by yamin_math Mentor
0 votes

(d)

Step 1:

The series is .

The above series have the common constant ratio.

So above series is in the form  of geometric series.

geometric series :

.

Where is first term

            is common ratio.

Common ratio .

Where is term .

            is term .

term in geometric series .

Step 2:

.

Now compare the above equation with geometric series.

The first term in the given series is image.

Common ratio .

image

In the given series image is the term.

But term in geometric series .

image

As base are equal , equate powers.

image

So ,the series has image terms .

Solution :

The series is in the form  of geometric series.

answered Jan 30, 2015 by yamin_math Mentor
0 votes

(e)

Step 1:

The series is .

The arithmetic series have the common difference.

The geometric series have the common ratio.

But the above series does not have common difference as well as common ratio.

We can notice that the series is made up by the squares of consecutive numbers.

Rewrite the series

image

So the term in the series is image.

image.

Solution :

The series is neither arithmetic series nor geometric series.

answered Jan 30, 2015 by yamin_math Mentor

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