# Common Core: High School - Algebra : Derive the Sum of a Finite Geometric Series Formula to Solve Problems: CCSS.Math.Content.HSA-SSE.B.4

## Example Questions

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### Example Question #1 : Derive The Sum Of A Finite Geometric Series Formula To Solve Problems: Ccss.Math.Content.Hsa Sse.B.4

Identify the following sequence as arithmetic, geometric, or neither.

Neither

Geometric

Arithmetic

Arithmetic

Explanation:

To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.

Looking at the given sequence,

subtract the first term from the second term to find the common difference.

From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.

Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.

### Example Question #2 : Derive The Sum Of A Finite Geometric Series Formula To Solve Problems: Ccss.Math.Content.Hsa Sse.B.4

Identify the following sequence as arithmetic, geometric, or neither.

Geometric

Arithmetic

Neither

Arithmetic

Explanation:

To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.

Looking at the given sequence,

subtract the first term from the second term to find the common difference.

From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.

Adding the common difference to each term in the sequence results in the next term in the sequence which makes this particular sequence, arithmetic.

### Example Question #3 : Derive The Sum Of A Finite Geometric Series Formula To Solve Problems: Ccss.Math.Content.Hsa Sse.B.4

Identify the following sequence as arithmetic, geometric, or neither.

Neither

Geometric

Arithmetic

Neither

Explanation:

To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.

Looking at the given sequence,

subtract the first term from the second term to find the common difference.

From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.

If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.

All terms except for the third term follow this therefore, the sequence is neither arithmetic nor geometric.

### Example Question #4 : Derive The Sum Of A Finite Geometric Series Formula To Solve Problems: Ccss.Math.Content.Hsa Sse.B.4

Identify the following sequence as arithmetic, geometric, or neither.

Geometric

Arithmetic

Neither

Neither

Explanation:

To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.

Looking at the given sequence,

subtract the first term from the second term to find the common difference.

From here, add the common difference to the second term. If the sum is the third term, then the sequence is arithmetic.

If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.

All terms except for the third term follow this therefore, the sequence is neither arithmetic nor geometric.

### Example Question #5 : Derive The Sum Of A Finite Geometric Series Formula To Solve Problems: Ccss.Math.Content.Hsa Sse.B.4

Identify the following sequence as arithmetic, geometric, or neither.

Arithmetic

Geometric

Neither

Neither

Explanation:

To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.

Looking at the given sequence,

subtract the first term from the second term to find the common difference.

From here, add the common difference to the second term.

If adding the common difference to each term in the sequence results in next term then the sequence is arithmetic.

All terms except for the fourth term follow this therefore, the sequence is neither arithmetic nor geometric.

### Example Question #6 : Derive The Sum Of A Finite Geometric Series Formula To Solve Problems: Ccss.Math.Content.Hsa Sse.B.4

Identify the following sequence as arithmetic, geometric, or neither.

Arithmetic

Neither

Geometric

Geometric

Explanation:

To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.

Looking at the given sequence,

divide the second term by the first term to find the common ratio.

From here, multiply the common ratio by each term to get the next term in the sequence.

Since each term is found by multiplying the common ratio with the previous term, the sequence is known as a geometric one.

### Example Question #7 : Derive The Sum Of A Finite Geometric Series Formula To Solve Problems: Ccss.Math.Content.Hsa Sse.B.4

Identify the following sequence as arithmetic, geometric, or neither.

Neither

Geometric

Arithmetic

Geometric

Explanation:

To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.

Looking at the given sequence,

divide the second term by the first term to find the common ratio.

From here, multiply the common ratio by each term to get the next term in the sequence.

Since each term is found by multiplying the common ratio with the previous term, the sequence is known as a geometric one.

### Example Question #8 : Derive The Sum Of A Finite Geometric Series Formula To Solve Problems: Ccss.Math.Content.Hsa Sse.B.4

Identify the following sequence as arithmetic, geometric, or neither.

Geometric

Neither

Arithmetic

Geometric

Explanation:

To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means there exists a common difference between the terms. If a sequence is geometric, then there exists a common ratio between the terms.

Looking at the given sequence,

divide the second term by the first term to find the common ratio.

From here, multiply the common ratio by each term to get the next term in the sequence.

Since each term is found by multiplying the common ratio with the previous term, the sequence is known as a geometric one.

If you take out 30 year mortgage of $200,000 at 5% interest, what will your monthly payment be? Possible Answers: Correct answer: Explanation: To solve for the monthly mortgage payment there are three steps that need to be followed. 1. Calculate the total amount that will be owed. This means applying the interest to the principal for the new total balance. Use the following formula to calculate the new total balance. Recall that the interest needs to be in decimal format. 2. Calculate how many months are in the desired amount of years. Recall that one year contains 12 months. 3. Divide the total balance by the number of months. ### Example Question #10 : Derive The Sum Of A Finite Geometric Series Formula To Solve Problems: Ccss.Math.Content.Hsa Sse.B.4 If you take out 15 year mortgage of$75,000 at 3% interest, what will your monthly payment be?

Explanation:

To solve for the monthly mortgage payment there are three steps that need to be followed.

1. Calculate the total amount that will be owed. This means applying the interest to the principal for the new total balance.

Use the following formula to calculate the new total balance.

Recall that the interest needs to be in decimal format.

2. Calculate how many months are in the desired amount of years.

Recall that one year contains 12 months.

3. Divide the total balance by the number of months.

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