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Flashcards: 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.

$\displaystyle -10,-4,2,8,14,...$

Arithmetic

Neither

Geometric

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All Common Core: High School - Algebra Resources

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Flashcards: 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.

$\displaystyle -10,-4,2,8,14,...$

Arithmetic

Neither

Geometric

Report an Error Copyright Notice

Flashcards: 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.

$\displaystyle -10,-4,2,8,14,...$

Your answer:

Neither

Your answer:

Geometric

Correct answer:

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,

$\displaystyle -10,-4,2,8,14,...$

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

$\text{Common Difference: }-4-(-10)=-4+10=6$ $\displaystyle \text{Common Difference: }-4-(-10)=-4+10=6$

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.

$\\-4+6=2 \\2+6=8 \\8+6=14$ $\displaystyle \\-4+6=2 \\2+6=8 \\8+6=14$

Flashcards: 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.

$\displaystyle 2,12,22,32,42,...$

Arithmetic

Neither

Geometric

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Flashcards: 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.

$\displaystyle 2,12,22,32,42,...$

Your answer:

Neither

Your answer:

Geometric

Correct answer:

Arithmetic

Explanation:

Looking at the given sequence,

$\displaystyle 2,12,22,32,42,...$

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

$\text{Common Difference: }12-2=10$ $\displaystyle \text{Common Difference: }12-2=10$

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.

$\\12+10=22 \\22+10=32 \\32+10=42$ $\displaystyle \\12+10=22 \\22+10=32 \\32+10=42$

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

All Common Core: High School - Algebra Resources

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

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

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

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

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