Terms in a Series - Pre-Calculus

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

For the 15th term, .

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.

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

.

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.

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.

The pattern in this arithmetic series is that each term is created by adding 4 to the previous one. You can then continue the series by continuing to add 4s until you've gotten to the tenth term:

1, 5, 9, 13, 17, 21, 25, 29, 33, 37

The correct answer, then, is 37.

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

For the 15th term, .

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.

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

.

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.

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.

The pattern in this arithmetic series is that each term is created by adding 4 to the previous one. You can then continue the series by continuing to add 4s until you've gotten to the tenth term:

1, 5, 9, 13, 17, 21, 25, 29, 33, 37

The correct answer, then, is 37.

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

For the 15th term, .

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.

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

.

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.

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.

The pattern in this arithmetic series is that each term is created by adding 4 to the previous one. You can then continue the series by continuing to add 4s until you've gotten to the tenth term:

1, 5, 9, 13, 17, 21, 25, 29, 33, 37

The correct answer, then, is 37.

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

For the 15th term, .

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.