Worksheet: Sum of an Infinite Geometric Sequence

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

Q1:

Express 0.375 as a common fraction.

  • A 1 2 5 3 3 3
  • B 1 2 5 3 3 3
  • C 1 , 2 5 0 3 3 3
  • D 3 7 5 1 , 0 0 1

Q2:

Express 3.72 as a common fraction.

  • A 2 5 1 1
  • B 2 4 1 1
  • C 1 2 4 3 3
  • D 4 1 1 1
  • E 4 1 3 1 1 1

Q3:

Express 0.433 as a common fraction.

  • A 1 3 3 0
  • B 1 5 0
  • C 4 3 7 1 , 0 1 0
  • D 1 1 3 0
  • E 4 3 3 9 9 0

Q4:

Express 26.9 as a rational number.

  • A3
  • B 1 3
  • C27
  • D 1 2 7
  • E 1 2

Q5:

Express 0.13+0.732 as a common fraction.

  • A 1 , 0 1 6 4 9 5
  • B 8 6 9 1 , 0 1 0
  • C 5 9 1 1 0
  • D 1 9 2 2

Q6:

Write 2.7 as a mixed number.

  • A 7 7 1 0
  • B 7
  • C 2 7 1 0
  • D 2 1 7
  • E 2 7 9

Q7:

Express 4.1 as a common fraction.

  • A 3 5 9
  • B 4 9
  • C 4 1 9
  • D 3 7 9
  • E 4 0 6 9 9

Q8:

Express 1.42 as a common fraction.

  • A 6 2 4 5
  • B 7 2 2 5
  • C 7 1 4 5
  • D 6 4 4 5
  • E 7 0 3 4 9 5

Q9:

Express 2.83 as a common fraction.

  • A 8 3 3 0
  • B 7 7 5
  • C 2 8 3 9 0
  • D 1 7 6
  • E 4 6 7 1 6 5

Q10:

Express 3.61 as a common fraction.

  • A 3 2 3 9 0
  • B 1 2 5
  • C 3 6 1 9 0
  • D 6 5 1 8
  • E 1 , 7 8 7 4 9 5

Q11:

Express 0.158 as a common fraction.

  • A 1 5 8 9 9 9
  • B 1 5 8 9 9 9
  • C 1 , 5 8 0 9 9 9
  • D 1 5 8 1 , 0 0 1

Q12:

Express 2.548 as a common fraction.

  • A 8 0 9 3 3 0
  • B 4 3 3
  • C 1 , 2 7 4 4 9 5
  • D 8 4 1 3 3 0
  • E 1 , 6 9 7 6 6 6

Q13:

Express 0.22+0.294 as a common fraction.

  • A 1 , 2 4 7 4 9 5
  • B 2 5 8 5 0 5
  • C 5 8 4 9 5
  • D 2 5 6 4 9 5

Q14:

Express 0.84+0.267 as a common fraction.

  • A 9 6 3 1 1 0
  • B 1 , 1 0 9 1 , 0 1 0
  • C 7 0 9 9 9 0
  • D 2 2 1 1 9 8

Q15:

Express 0.16+0.946 as a common fraction.

  • A 1 , 2 7 3 4 9 5
  • B 2 2 3 2 0 2
  • C 1 3 7 1 9 8
  • D 1 , 0 9 7 9 9 0

Q16:

Express 0.63+0.916 as a common fraction.

  • A 3 2 8 4 5
  • B 3 1 1 2 0 2
  • C 4 9 1 9 8
  • D 1 , 5 3 7 9 9 0

Q17:

Express 0.02+0.948 as a common fraction.

  • A 5 7 4 4 9 5
  • B 9 7 7 1 , 0 1 0
  • C 8 2 3 9 9 0
  • D 9 5 9 9 9 0

Q18:

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

  • A 8 × 6
  • B 1 2 8 , 3 2 8 , 9 2 8 ,
  • C 2 6 3 , 7 8 9 5 , 2 , 3 6 7 2 5 ,
  • D 5 1 0 , 6 8 0 , 2 , 7 2 0 3 ,
  • E 5 1 0 , 6 8 0 , 2 , 7 2 0 3 ,

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 𝑎 = 6 , 1 8 , 5 4 , , 𝑆 = 3 2
  • B 𝑎 = 3 2 , 8 , 2 , , 𝑆 = 1 2 8 5
  • C 𝑎 = 3 2 , 8 , 2 , , 𝑆 = 1 2 8 3
  • D 𝑎 = 3 6 , 1 2 , 4 , , 𝑆 = 5 4
  • E 𝑎 = 3 6 , 1 2 , 4 , , 𝑆 = 3 2

Q20:

Find the sum of an infinite number of terms of a geometric sequence starting from the third term given the third term is 1372 and the sixth term is 13576.

  • A 1 3 2 7
  • B 1 3 2 1 6
  • C 1 3 1 0 8
  • D 1 3 5 4
  • E 2 6 2 7

Q21:

Consider the series 4+𝑦+𝑦+𝑦+𝑦+.

Is this series geometric?

  • Ano
  • Byes

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

  • A 4 + 3 𝑦 1 𝑦
  • B 4 3 𝑦 1 + 𝑦
  • C 4 3 𝑦 1 𝑦
  • D 3 4 𝑦 1 + 𝑦
  • E 4 + 3 𝑦 1 + 𝑦

Q22:

Find how many terms should be taken from the geometric sequence (0.3,0.9,2.7,) starting from the first term to make the sum 327.9.

Q23:

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

Find the first three terms and the sum to infinity (𝑆) of the infinite geometric sequence with 𝑎𝑎=33 and 𝑆=132.

  • A 3 5 2 5 , 1 7 6 5 , 8 8 5 , , 𝑆 = 7 0 4 5
  • B 5 2 8 7 , 2 6 4 7 , 1 3 2 7 , , 𝑆 = 1 , 0 5 6 7
  • C 1 1 1 0 , 1 1 5 , 2 2 5 , , 𝑆 = 1 1 5
  • D 3 5 2 5 , 1 7 6 5 , 8 8 5 , , 𝑆 = 7 0 4 1 5

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 𝑎 = 1 3 3 , 1 3 6 , 1 3 1 2 , , 𝑆 = 2 0 8 3
  • B 𝑎 = 5 2 3 , 1 0 4 3 , 2 0 8 3 , , 𝑆 = 5 2 3
  • C 𝑎 = 1 0 4 3 , 5 2 3 , 2 6 3 , , 𝑆 = 2 0 8 3
  • D 𝑎 = 2 6 3 , 5 2 3 , 1 0 4 3 , , 𝑆 = 5 2 3

Q25:

Find the sum of an infinite geometric sequence given the first term is 171 and the fourth term is 17164.

  • A 5 7
  • B228
  • C 5 7 1 6
  • D 6 8 4 5
  • E 5 7 6 4

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