It will be helpful if you can see that the sequence is changing by -6 to get to each number. The quickest way to solve this is to keep going with the sequence by subtracting six from each number to get to the next number.

9, 3, -3, -9, -15, -21, -27, -33, -39, -45

-45 is the 10th number in the sequence.

Another way to find the 10th term is by using the equation for arithmetic sequences.

whereis the term in question,is the first term,is the numbered term, andis the difference of the terms.

To find d subtract the first two terms.

Therefore, the equation becomes

Step 1: We know it's a geometric sequence, so the difference between each consecutive term is the same. We must find the difference.



Step 2: For every term after the first term, we will add a multiple ofto the first term.

Step 3: We can write an equation that helps us find the nth term of the sequence. We add a multiple of 4n to 5; the equation becomes.

Step 4: We need to find the value of n. We want the 15th number and we are given the first number. There arenumbers in between, so n=14.

Step 5: Plug in 14 for n and find the 15th term



Theterm is

Step 1: We need to find the difference between the terms. To find the difference, subtract the first two terms.

Difference=

Step 2: To find the next term of a arithmetic sequence, we add the difference to the previous term.

Fourth term=term+5
term=. The fourth term is 19.

Step 3: To find theterm, we must add a multiple ofto the first term. In this problem, we are given theterm, so we need to find how many terms are in between theandterm.

. This tells me that I have to addfourteen times to get to theterm..

Step 4: Now that we know what the value of n, we can plug it in to the equation:

, where 4 is the starting number, and n represents how many times I need to add 5 to the next term (and up to the 15th term).

Let's plug it in:

.

So, theterm in this sequence is.

Step 1: Try to find a pattern in the sequence

The pattern is decreasing perfect squares, the difference between each base of the consecutive term is..

Step 2: Find the next term...

If the base of the next term goes down by, the next term is..



The next term of this sequence is.

Step 1: Try to find the difference between the terms.

Difference betweenandis.
Difference betweenandis.
Difference betweenandis.

Difference betweenandis.

The difference between consecutive numbers is an odd number, and the difference between the consecutive terms is always..

The difference betweenandis



The next number in the sequence is.

Step 1: Find the next term in the sequence:

Step 2: Can you recognize the sequence here??

This is the Fibonacci Sequence.. The sum of the previous two terms is equal to the next consecutive term..







The missing term is 13.

Step 1: Find the difference between each two consecutive terms...

The difference is always 6 because we have a sequence...

Step 2: Find the next term in the sequence..



The next term is.

Step 1: Calculate the difference between the terms...

, add 9
, add 9
, add 9

Step 2: We found the pattern between the terms..

So, we can add 9 to the term before theto find the value of..



The missing term (the next term) in the sequence is.

Step 1: Find the difference between each term...

Subtract the first term from the third term...


There are two terms between first and third...Take the answer in step 1 and divide by 2 to get the difference between consecutive terms...



The common difference is.

Step 2: Find an equation that describes the sequence....

The equation is, whererepresents how many terms I need to calculate andis the first term...

Step 3: Plug in...

To find n, we subtract the term that we want from the original term...

So, if we want theth term and we are given the first term...

Then

So,

Theth term is.

Step 1: Find the successive difference rows until we get equal values between every two consecutive numbers.

Step 2: Since we obtain equal values for the successive differences in the second row, hence theterm of the sequence is a second-degree polynomial.

So, theterm takes the form of

Step 3: Now, substitutinginto the formula, we get:

Step 4: Solve the system of linear equations:

So, theterm takes the form:

Step 5: Plug ininto the form...