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IPMAT Rohtak Sequences and Series Gp — practice questions

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

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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.

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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.

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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.

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More Mathematics topics

Binomial TheoremSequences and SeriesGeometryProbability & StatisticsSequencesPermutations and CombinationsCorrelation and RegressionLinear Programming