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+6where kkk is a constant. Given that the number of new users joining each month is modeled as a geometric series,
show that k2−5k−84=0k^2 - 5k - 84 = 0k2−5k−84=0.
Predict the number of new premium users joining in the 6th month.
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.
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.