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1.6 Sequences and Series

1.6 Sequences and Series

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Question 182

A subscription-based fitness app tracks the number of new premium users each month. In the first three months after a major update, the number of new premium users, in thousands, was recorded as:

3k−28,k,k+6 3k - 28, \quad k, \quad k + 6 3k−28,k,k+6

where kkk is a constant. Given that the number of new users joining each month is modeled as a geometric series,

a.

show that k2−5k−84=0k^2 - 5k - 84 = 0k2−5k−84=0.

[3]
b.

Predict the number of new premium users joining in the 6th month.

[2]
c.

The total number of all premium users who have joined the app since the update is predicted to exceed 5 million for the first time in the NNNth month.

Calculate the value of NNN according to the model.

[4]
Markscheme

1.6 Sequences and Series Questions

  1. A Level
  2. /Maths
  3. /1.6 Sequences and Series

308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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