Transcript Lesson One Introduction to APs and GPs File

Introduction to APs
and GPs Questions
State whether the given sequence is arithmetic, geometric or neither.
Find a formula for t n , the nth term of each sequence.
a)
1 2 3 4
, , , ...
2 3 4 5
a a 2 a3 a 4
, , , ...
b)
9 18 36 72
n
n 1
Neither an AP or
GP, the rule is:
This is a GP and
the rule is:
2
9
( )
a n
2
Find the first term of the arithmetic sequence where
t8  25, t20  61
Solution: The first term is 4
Find the number of multiples of 6 between 28 and 280.
Solution: There are 42 multiples of 6
How many four digit numbers are not divisible by 11?
Solution: 8181 numbers are not divisible by 11
True or false? If the sequence a, b, c is
a
b
c
2
,
2
,
2
arithmetic, then the sequence
is
geometric.
Solution: True
xy
2
y
,
2
xy
,
2,
Find x and y if the sequence
2 ,....
is geometric.
Solution:
Find x if the sequence
x   12 , y  4
4, x, 32 x is
a) arithmetic and b) geometric
Solution: a) 8 b) 6
Assuming that a and b are positive, find x if the sequence a, x, b
is:
a) arithmetic
b) geometric
ab
2
 a b
A man of mass 90 kg plans to diet and to reduce his mass to 72 kg in
four weeks by a constant percentage reduction each day. What
should his mass be 1 week after starting his diet? (Leave your
answer correct to 3 significant figures.)
Answer: 85.1 kg
Find the possible values for the constants a and c (a < c),
given that a,12, c are consecutive terms of a G.P. and a,
20, c are consecutive terms of an A.P.
Answer: c = 36, a = 4