1. Sequences : Extra problems
By the end of this lesson you will be able to:
• Solve exam problems about sequences.
1

2. Find the sum of the positive terms of the arithmetic
sequence 85, 78, 71, ....
Answer: 559
2

3. Evaluate
Answer: 118096
3

4. Evaluate
Answer: 584
4

5. Find the sum to infinity of the geometric series
Answer: ­36/5
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
6

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
7

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
8

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= 2
b= ­3
9

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. A=5000(1.063)n
(b) What will be the value of the investment at the
end of five years?
$6786.35
(c) The value of the investment will exceed
$ 10 000 after n full years.
(i) Write an inequality to represent this
information. 10000<5000(1.063)n
(ii)Calculate the minimum value of n.
12
10

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
11