Question
[Maximum mark: 8]
Consider the geometric sequence 10, 5, 2.5, 1.25, …
(a) Express the general term nu in terms of n . [1]
(b) Find the first term which is smaller than 10-3 = 0.001. [3]
(c) Find the sum of the first 20 terms correct to 6 decimal places. [2]
(d) Find the sum of the infinite series.
Answer/Explanation
Answer:
(a) 10 x 0.5n-1 (= 20 x 0.5n )
(b) 0.000610
(c) 19.999981
(d) 20
Question
Maximum mark: 5]
Consider the infinite geometric sequence 3, 3(0.9), 3(0.9)2, 3(0.9)3, … .
(a) Write down the 10th term of the sequence. Do not simplify your answer. [1]
(b) Find the sum of the infinite sequence. [4]
Answer/Explanation
Answer:
a. \(u^{10}=3(0.9)^{9}\)
b. \(S=\frac{3}{1-0.9}=\frac{3}{0.1}=30\)
Question
[Maximum mark: 6]
Consider the infinite geometric series 405 + 270 + 180 +….
(a) For this series, find the common ratio, giving your answer as a fraction in its simplest form. [2]
(b) Find the fifteenth term of this series. [2]
(c) Find the exact value of the sum of the infinite series. [2]
Answer/Explanation
Answer
a. \(r=\frac{2}{3}\)
b. u15 = 1.39
c. S = 1215
Question
[Maximum mark: 6]
An infinite geometric sequence has first term u1 and common ratio r . Find the values of u1 and of r given that S3 = 35 and S∞ = 40.
Answer/Explanation
Answer:
\(r=\frac{1}{2}, u_{1}=20\)