# Worksheet: Sum of an Infinite Geometric Sequence

In this worksheet, we will practice calculating the sum of an infinite geometric sequence.

Q1:

Express as a common fraction.

• A
• B
• C
• D

Q2:

Express as a common fraction.

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• B
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• D
• E

Q3:

Express as a common fraction.

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• C
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• E

Q4:

Express as a rational number.

• A3
• B
• C27
• D
• E

Q5:

Express as a common fraction.

• A
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• C
• D

Q6:

Write as a mixed number.

• A
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• E

Q7:

Express as a common fraction.

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• E

Q8:

Express as a common fraction.

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• D
• E

Q9:

Express as a common fraction.

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• E

Q10:

Express as a common fraction.

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• E

Q11:

Express as a common fraction.

• A
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• D

Q12:

Express as a common fraction.

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• B
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• D
• E

Q13:

Express as a common fraction.

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• B
• C
• D

Q14:

Express as a common fraction.

• A
• B
• C
• D

Q15:

Express as a common fraction.

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• D

Q16:

Express as a common fraction.

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• B
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• D

Q17:

Express as a common fraction.

• A
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• C
• D

Q18:

Which of the following geometric sequences can be summed up to infinity?

• A
• B
• C
• D
• E

Q19:

Find the geometric sequence and the sum to infinity given the sum of the first three terms equals 42, the first term exceeds the second term by 24, and all terms are positive.

• A,
• B,
• C,
• D,
• E,

Q20:

Find the sum of an infinite number of terms of a geometric sequence starting from the third term given the third term is and the sixth term is .

• A
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• E

Q21:

Consider the series .

Is this series geometric?

• Ano
• Byes

The series is convergent for some . What does it converge to in those cases? Give a simplified answer.

• A
• B
• C
• D
• E

Q22:

Find how many terms should be taken from the geometric sequence starting from the first term to make the sum 327.9.

Q23:

The term of a geometric sequence is , first term is , and the sum of the first terms is .

Find the first three terms and the sum to infinity of the infinite geometric sequence with and .

• A,
• B,
• C,
• D,

Q24:

Find the infinite geometric sequence and the sum to infinity given the sum of the first and second terms is 52, the sum of the third and fourth terms is 13, and all terms are positive.

• A,
• B,
• C,
• D,

Q25:

Find the sum of an infinite geometric sequence given the first term is 171 and the fourth term is .

• A
• B228
• C
• D
• E