Skip to content

Course home

Sign up

1.6 Sequences and Series

EasyMediumHard
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950
Question 10

In a geometric sequence x1,x2,x3,…x_1, x_2, x_3, \dotsx1​,x2​,x3​,…:

  • the common ratio is rrr
  • x2+x3=9x_2 + x_3 = 9x2​+x3​=9
  • x4=6x_4 = 6x4​=6
a.

Show that r r\,r satisfies the equation

3r2−2r−2=0 3r^2 - 2r - 2 = 0 3r2−2r−2=0
[4]
b.

Given that the geometric sequence has a sum to infinity,

find the exact value of x1 x_1\,x1​ in the form a+b7a + b\sqrt{7}a+b7​ where a,b∈Qa, b \in \mathbb{Q}a,b∈Q.

[4]
c.

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

[2]
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.

Question bank