Derive the Sum of a Finite Geometric Series Formula to Solve Problems: CCSS.Math.Content.HSA-SSE.B.4

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Algebra › Derive the Sum of a Finite Geometric Series Formula to Solve Problems: CCSS.Math.Content.HSA-SSE.B.4

Questions 1 - 10
1

Identify the following sequence as arithmetic, geometric, or 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,

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.

2

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

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,

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.

3

Identify the following sequence as arithmetic, geometric, or 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,

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.

4

What type of sequence describes the following set of numbers?

3, 15, 75, 375, 1875

Geometric Series

Arithmetic Series

Unknown Series

Explanation

This is a geometric series. The same value, 5, is multiplied by each value to get to the next:

3 x 5 = 15

15 x 5 = 75

75 x 5 = 375

375 x 5 = 1875

When each term in a series is equal to the previous term multiplied by the same factor - in this case 5 - that's a geometric series.

5

1, 9, 81, 729, 6561...

Is the sequence above arithmetic, geometric, or neither?

Geometric

Arithmetic

Neither

Explanation

The series is geometric, which means that to get from one value to the next you always multiply by the same value. Here to get from one value to the next, you multiply by 9 each time:

1 x 9 = 9

9 x 9 = 81

81 x 9 = 729

729 x 9 = 6561

6

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

Arithmetic

Geometric

Neither

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.

7

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

Arithmetic

Geometric

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.

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

8

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

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

Arithmetic

Geometric

Neither

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.

9

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

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,

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.

10

Identify the following sequence as arithmetic, geometric, or 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,

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.

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