Skip to content

Course home

Sequences and Series

Sequences and Series

EasyMediumHard
123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159
Question 89

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

Sequences and Series Questions

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

178 exam-style questions on Edexcel A Level Maths Sequences and Series, covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series. Each one has a worked solution and a mark scheme showing where the marks go.

Question bank