Lesson Worksheet: Infinite Geometric Series Mathematics • 10th Grade

In this worksheet, we will practice determining whether a geometric series is convergent and finding its limit.

Q1:

Can the sum of an infinite geometric series with common ratio 𝑟 be found when |𝑟|<1?

  • ANo
  • BYes

Q2:

Find the sum of the infinite geometric sequence 49,21,9,.

  • A14710
  • B3433
  • C21
  • D3434
  • E34310

Q3:

Can the sum of an infinite geometric series be found for any value of 𝑟 satisfying |𝑟|1?

  • AYes
  • BNo

Q4:

Find the possible infinite geometric series where the sum is 21 and the sum of the first and second terms is 353.

  • A17,221,463, or 135,2105,4315,
  • B7,143,289, or 35,703,1409,
  • C17,314,928, or 135,370,9140,
  • D7,212,634, or 35,1052,3154,

Q5:

Find the sum of an infinite number of terms of the geometric sequence 87,87,1,.

  • A868787+87
  • B878687+87
  • C87888787
  • D87868787
  • E878887+87

Q6:

Find the common ratio of an infinite geometric sequence given the sum is 52 and the first term is 14.

  • A267
  • B14
  • C1926
  • D3326

Q7:

Find the infinite geometric sequence given each term of the sequence is twice the sum of the terms that follow it and the first term is 37.

  • A37,373,379,
  • B111,37,373,
  • C37,111,333,
  • D37,373,379,
  • E111,37,373,

Q8:

Find the sum of an infinite number of terms of a geometric sequence given the first term is 265 and the fourth term is 650343.

  • A63725
  • B915
  • C9130
  • D637150
  • E136

Q9:

Find the sum of the infinite geometric sequence 7,(7),7,.

  • A64350
  • B1350
  • C1336
  • D748
  • E750

Q10:

Find the sum of the squares of the terms of an infinite geometric sequence given the first term is 49 and the common ratio is 9𝑥.

  • A2,401181𝑥
  • B2,40181𝑥1
  • C4919𝑥
  • D499𝑥
  • E2,40181𝑥

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