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.

  • A125333
  • B125333
  • C1,250333
  • D3751,001

Q2:

Express 3.72 as a common fraction.

  • A2511
  • B2411
  • C12433
  • D4111
  • E413111

Q3:

Express 0.433 as a common fraction.

  • A1130
  • B433990
  • C4371,010
  • D1330
  • E150

Q4:

Express 26.9 as a rational number.

  • A3
  • B13
  • C27
  • D127
  • E12

Q5:

Express 0.13+0.732 as a common fraction.

  • A1,016495
  • B8691,010
  • C59110
  • D1922

Q6:

Write 2.7 as a mixed number.

  • A7710
  • B7
  • C2710
  • D217
  • E279

Q7:

Express 4.1 as a common fraction.

  • A359
  • B49
  • C419
  • D379
  • E40699

Q8:

Express 1.42 as a common fraction.

  • A6245
  • B7225
  • C7145
  • D6445
  • E703495

Q9:

Express 2.83 as a common fraction.

  • A8330
  • B775
  • C28390
  • D176
  • E467165

Q10:

Express 3.61 as a common fraction.

  • A32390
  • B125
  • C36190
  • D6518
  • E1,787495

Q11:

Express 0.158 as a common fraction.

  • A158999
  • B158999
  • C1,580999
  • D1581,001

Q12:

Express 2.548 as a common fraction.

  • A809330
  • B433
  • C1,274495
  • D841330
  • E1,697666

Q13:

Express 0.22+0.294 as a common fraction.

  • A1,247495
  • B258505
  • C58495
  • D256495

Q14:

Express 0.84+0.267 as a common fraction.

  • A963110
  • B1,1091,010
  • C709990
  • D221198

Q15:

Express 0.16+0.946 as a common fraction.

  • A1,273495
  • B223202
  • C137198
  • D1,097990

Q16:

Express 0.63+0.916 as a common fraction.

  • A32845
  • B311202
  • C49198
  • D1,537990

Q17:

Express 0.02+0.948 as a common fraction.

  • A574495
  • B9771,010
  • C823990
  • D959990

Q18:

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

  • A8×6
  • B128,328,928,
  • C263,7895,2,36725,
  • D510,680,2,7203,
  • E510,680,2,7203,

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.

  • A𝑎=6,18,54,, 𝑆=32
  • B𝑎=32,8,2,, 𝑆=1285
  • C𝑎=32,8,2,, 𝑆=1283
  • D𝑎=36,12,4,, 𝑆=54
  • E𝑎=36,12,4,, 𝑆=32

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.

  • A1327
  • B13216
  • C13108
  • D1354
  • E2627

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.

  • A4+3𝑦1𝑦
  • B43𝑦1+𝑦
  • C43𝑦1𝑦
  • D34𝑦1+𝑦
  • E4+3𝑦1+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.

  • A3525,1765,885,, 𝑆=7045
  • B5287,2647,1327,, 𝑆=1,0567
  • C1110,115,225,, 𝑆=115
  • D3525,1765,885,, 𝑆=70415

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.

  • A𝑎=133,136,1312,, 𝑆=2083
  • B𝑎=523,1043,2083,, 𝑆=523
  • C𝑎=1043,523,263,, 𝑆=2083
  • D𝑎=263,523,1043,, 𝑆=523

Q25:

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

  • A57
  • B228
  • C5716
  • D6845
  • E5764

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