1

Sequences : Extra problems

By the end of this lesson you will be able to:

• Solve exam problems about sequences.

2

Find the sum of the positive terms of the arithmetic sequence 85, 78, 71, ....

Answer: 559

3

Evaluate

Answer: 118096

4

Evaluate

Answer: 584

5

Find the sum to infinity of the geometric series

Answer: ­36/5

6

Consider the infinite geometric series

(a) For what values of x does the series converge?(b) Find the sum of the series if x = 1.2.

a)

b) 5

7

Consider the arithmetic series 2 + 5 + 8 +....

(a) Find an expression for Sn, the sum of the first n terms.(b) Find the value of n for which Sn = 1365.

Sn=0.5n+1.5n2

n=30

8

A geometric sequence has all positive terms. The sum of the first two terms is 15 and the sum to infinity is 27. Find the value of(a) the common ratio;(b) the first term.

a)

b) 9

9

The first four terms of an arithmetic sequence are 2, a ­ b, 2a +b + 7, and a ­ 3b, where a and b are constants. Find a and b.

a= 2b= ­3

10

A sum of $ 5 000 is invested at a compound interest rate of 6.3 % per annum.(a) Write down an expression for the value of the investment after n full years.

(b) What will be the value of the investment at the end of five years?

(c) The value of the investment will exceed $ 10 000 after n full years.

(i)Write an inequality to represent this information. (ii)Calculate the minimum value of n.

A=5000(1.063)n

$6786.35

10000<5000(1.063)n

12

11

A man borrows $ 5000 at 18 % p.a. over a period of 5 years, with the interest compounding every month. Find to the nearest dollar the amount owing after 5 years.

$12 216.10