Precalculus : Sequences and Series

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #177 : Pre Calculus

Solve:  

Possible Answers:

Correct answer:

Explanation:

The summation starts at 2 and ends at 4.  Write out the terms and solve.

The answer is: 

Example Question #178 : Pre Calculus

Write the following series in sigma notation.

Possible Answers:

Correct answer:

Explanation:

To write in sigma notation, let's make sure we have an alternating sign expression given by:

Now that we have the alternating sign, let's establish a function that increases by  per term starting at . This is given by

Putting it all together,

 

Example Question #179 : Pre Calculus

Compute:  

Possible Answers:

Correct answer:

Explanation:

In order to solve this summation, substitute the bottom value of  to the function, plus every integer until the iteration reaches to 5.

Example Question #180 : Pre Calculus

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

To evaluate this, input the bottom integer into the expression . Repeat for every integer following the bottom integer until we reach to the top integer .  Sum each iteration.

Add these terms for the summation.

Example Question #21 : Sequences And Series

What is the proper sigma sum notation of the summation of  ?

Possible Answers:

Correct answer:

Explanation:

Given that the first term of the sequence is , we know that the first term of the summation must be , and thus the lower bound of summation must be equal to  There is only one option with this qualification, and so we have our answer.

Example Question #11 : Sequences And Series

Consider the sequence:

What is the fifteenth term in the sequence?

Possible Answers:

Correct answer:

Explanation:

The sequence can be described by the equation , where is the term in the sequence.

For the 15th term, .

Example Question #2 : Terms In A Series

What is the sum of the first  terms of an arithmetic series if the first term is , and the last term is ?

Possible Answers:

Correct answer:

Explanation:

Write the formula to find the arithmetic sum of a series where  is the number of terms,  is the first term, and  is the last term.

Substitute the given values and solve for the sum.

Example Question #3 : Terms In A Series

Given the terms of the sequence , what are the next two terms after ?

Possible Answers:

Correct answer:

Explanation:

The next two terms are  and . This is the Fibonacci sequence where you start off with the terms  and , and the next term is the sum of two previous terms. So then

and so on.

Example Question #21 : Sequences And Series

What is the fifth term of the series 

Possible Answers:

Correct answer:

Explanation:

Let's try to see if this series is a geometric series.

We can divide adjacent terms to try and discover a multiplicative factor.

Doing this it seems the series proceeds with a common multiple of  between each term.

Rewriting the series we get,

 .

When 

.

Example Question #22 : Sequences And Series

What is the 9th term of the series that begins 2, 4, 8, 16...

Possible Answers:

488

1024

512

256

144

Correct answer:

512

Explanation:

In this geometric series, each number is created by multiplying the previous number by 2.  You may also see that, because the first number is 2, it also becomes a list of powers of 2.  The list is 2, 4, 8, 16, 32, 64, 128, 256, 512, where you can see that the 9th term is 512.

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