Alevel_C1C2

13
Exam-style assessment
Sequences and series
1. (a) The first term in a geometric series is 4 and the common ratio is 1 2 .
Write down the first four terms in the series. (1)
(b) Find the sum of the first ten terms of this geometric series giving your answer
correct to four decimal places. (2)
(c) Determine the difference between the sum to infinity and the sum to ten terms
of this series giving your answer correct to four decimal places. (3)
2. (a) For the geometric series 5,
5
− ,
5
,
5
− find the common ratio. (2)
3 9 27
(b) Write down the next two terms in this series. (2)
(c) Find the sum to infinity of this series. (2)
3. (a) Write down all the terms in the expansion of (2 + x) 4 giving your answer in
the simplest form. (3)
(b) If terms involving x 3 and higher may be neglected show that
(1 + 2x)(2 + x) 4 » a + bx + cx 2
and find the values of the constants a, b and c. (3)
( )
4. (a) In the expansion of 1 −
x n the coefficient of x
2
2 is 9, where n is
a positive integer.
Find the value of n. (5)
(b) Using this value of n find the coefficient of the term in x 3 . (2)
5. (a) In the expansion of (1 + ax) 8 the third term is 448x 2 .
Find the value of the constant a. (3)
(b) Taking the first four terms in the expansion of (1 + ax) 8 and, using the value
of the constant a, find an approximate value of (1.4) 8 writing your result to
three decimal places. (6)
(c) What is the percentage error in taking this approximate value of (1.4) 8
compared with the exact value?
Write the percentage to the nearest integer. (2)
© Oxford University Press 2008
Core C2