# Precalculus : Sequences and Series

## Example Questions

### Example Question #177 : Pre Calculus

Solve:

Explanation:

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

### Example Question #178 : Pre Calculus

Write the following series in sigma notation.

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:

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:

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  ?

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?

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 ?

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 ?

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

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...

488

1024

512

256

144