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1.7 D: Sequences and series

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Question 180

A geometric sequence has first term aaa and common ratio rrr, where r>0r > 0r>0.

Given that

  • the 2nd term is 12
  • the 4th term is 6.75
a.

Show that r=0.75r = 0.75r=0.75.

[2]
b.

Hence find the value of aaa.

[1]
c.

Given that the sum of the first nnn terms of this sequence is greater than 63.5

Find the smallest possible value of nnn.

(Solutions based entirely on graphical or numerical methods are not acceptable.)

[5]

1.7 D: Sequences and series Questions

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

Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.

Question bank

1.4 A: Proof
1.5 B: Algebra and functions
1.6 C: Coordinate geometry in the (x, y) plane
1.7 D: Sequences and series
1.8 E: Trigonometry
1.9 F: Exponentials and logarithms
1.10 G: Differentiation
1.11 H: Integration
1.12 I: Numerical methods (A-level only)
1.13 J: Vectors