Skip to content

Course home

Sign up

1.7 D: Sequences and series

EasyMediumHard
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950
Question 8

A company’s net cash flow in year nnn, denoted by PnP_nPn​ (in millions of dollars), follows a geometric progression with common ratio rrr.

You are given that:

  • The sum of the cash flows in the second and third years is P2+P3=10P_2 + P_3 = 10P2​+P3​=10
  • The cash flow in the fourth year is P4=20P_4 = 20P4​=20
a.

Show that r r\,r satisfies the equation r2−2r−2=0r^2 - 2r - 2 = 0r2−2r−2=0.

[4]
b.

Given that the sum of the cash flows over an infinite time period, ∑n=1∞Pn\sum_{n=1}^{\infty} P_n∑n=1∞​Pn​, is convergent,

find the exact value of P1P_1P1​.

[4]
c.

Hence, calculate the exact value of S∞S_\inftyS∞​.

[3]
Markscheme

1.7 D: Sequences and series Questions

  1. A Level
  2. /Maths
  3. /1.7 D: Sequences and series

308 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

Question bank