Start learning →

TISSNET Sequences and Series Gp — practice questions

Explore 52 free Sequences and Series Gp questions in TISSNET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Sequences and Series Gp with Quill →

Sequences and Series Gp questions and exercises with answers

Showing questions 1–30 of 52.

In a geometric progression (GP) with first term a and common ratio r, the nth term aₙ isRead the answer and worked solution →The common ratio of the GP 5, 25, 125, … isRead the answer and worked solution →The sum of the first n terms of a GP (a, ar, ar², …) when r ≠ 1 isRead the answer and worked solution →If aₙ = 2n + 5, then a₁, a₂, a₃ areRead the answer and worked solution →The Fibonacci sequence is defined by a₁ = a₂ = 1 and aₙ = a_{n−1} + a_{n−2}. Its first five terms areRead the answer and worked solution →Which term of the GP 2, 8, 32, … equals 131072?Read the answer and worked solution →In a GP, the 3rd term is 24 and the 6th term is 192. The 10th term isRead the answer and worked solution →The sum to 5 terms of the GP 1 + 2/3 + 4/9 + … isRead the answer and worked solution →The sum to infinity of the GP a + ar + ar² + … exists if and only ifRead the answer and worked solution →Which expression gives the sum to infinity of 1 + 1/2 + 1/4 + 1/8 + …?Read the answer and worked solution →In a GP, the sum of the first three terms is 13/12 and their product is −1. The common ratio isRead the answer and worked solution →How many terms of the GP 3, 3/2, 3/4, … sum to 3069/512?Read the answer and worked solution →Sum to n terms of the series 7 + 77 + 777 + … equalsRead the answer and worked solution →The 20th term of the sequence aₙ = (n − 1)(2 − n)(3 + n) isRead the answer and worked solution →Spot the term that breaks the progressionRead the answer and worked solution →Next Term in Sequence (ISC 12)Read the answer and worked solution →Match each series word to its meaningRead the answer and worked solution →Complete the arc length relationRead the answer and worked solution →Match each identity to its nameRead the answer and worked solution →The Pythagorean identitiesRead the answer and worked solution →Odd function or even function?Read the answer and worked solution →Complete the degree and radian conversionRead the answer and worked solution →True or false: identities and parityRead the answer and worked solution →Match each sum or difference formula to its resultRead the answer and worked solution →Signs in the expansionRead the answer and worked solution →Which formula does this belong to?Read the answer and worked solution →True or false: periodicityRead the answer and worked solution →Complete the complementary angle rulesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →

Worked practice questions

In a geometric progression (GP) with first term a and common ratio r, the nth term aₙ is

  1. a + (n − 1)r
  2. a · rⁿ
  3. a · r^(n−1)
  4. a · n · r
Show answer and solution

Correct answer: C. a · r^(n−1)

aₙ = a · r^(n−1). Compare with an AP whose nth term is a + (n−1)d.

Open this question →

The common ratio of the GP 5, 25, 125, … is

  1. 3
  2. 5
  3. 1/5
  4. 25
Show answer and solution

Correct answer: B. 5

We have r = 25/5. That is r = 125/25. So r = 5.

Open this question →

The sum of the first n terms of a GP (a, ar, ar², …) when r ≠ 1 is

  1. S_n = a · (1 − rⁿ) / (1 − r)
  2. S_n = a + (n − 1)r
  3. S_n = a · r^(n−1)
  4. S_n = n(n + 1)/2
Show answer and solution

Correct answer: A. S_n = a · (1 − rⁿ) / (1 − r)

S_n = a(1 − rⁿ)/(1 − r), equivalent to a(rⁿ − 1)/(r − 1) for |r| ≠ 1.

Open this question →

How to practise

  1. Choose a Sequences and Series Gp question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

More Mathematics topics

Binomial TheoremSequences and SeriesGeometryProbability & StatisticsSequencesPermutations and CombinationsCorrelation and RegressionLinear Programming