# 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

### 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.

Arithmetic

Neither

Geometric

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.

Arithmetic

Geometric

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.

Geometric

Neither

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.

Geometric

Neither

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 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.

Geometric

Arithmetic

Neither

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.

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 #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.

Arithmetic

Geometric

Neither

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 #9 : 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

Arithmetic

Explanation:

To identify the sequence as either arithmetic or geometric, first recall the difference between the two. An arithmetic sequence means that there is a common difference between the terms. If a sequence is geometric, then there is 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 #10 : Derive The Sum Of A Finite Geometric Series Formula To Solve Problems: Ccss.Math.Content.Hsa Sse.B.4

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

100, 200, 300, 400, 500...

Arithmetic

Neither

Geometric

Arithmetic

Explanation:

This is an arithmetic sequence. Note that the same number (100) is added to each value in the set to give us our next number:

100

100 + 100 = 200

200 + 100 = 300

300 + 100 = 400

400 + 100 = 500

When the same value is added to each term to determine the next one, that is an arithmetic sequence.