Question 1
1(a):
Given the sequence,
3, 6, 11, 18,what is the next term?
ANSWER: Multiple Choice (Type 1)
A: 23
B: 25
C: 27
D: 29
Answer: C
Workings:
Quadratic sequence is n^2+2
5^2+2=27
Marks= 1
1(b):
Consider the following quadratic sequence
n^2+4n-7What is the 5^{th} term in the sequence?
ANSWER: Multiple Choice (Type 1)
A: 38
B: 18
C: 52
D: 12
Answer: A
Workings:
Substitute n=5 into n^{th}term
5^2 + 4 \times 5 - 7 = 38
Marks= 1
1(c):
Choose the quadratic sequence from the list of sequences below.
ANSWER: Multiple Choice (Type A)
A: 7, 0, -5, -8, -9
B: 1,1, 2, 3, 5
C: 2, 8, 11, 14, 17
D: 3, 5, 7, 10
Answer: A
Workings:
A is the only answer with a constant 2^{nd} difference = 2
Quadratic Sequence is x^2-10x+16
Marks= 1
Question 2
Use the following quadratic equation:
n^2+6n -102(a):
List the first 5 terms in the sequence.
ANSWER: Multiple Answers (Type 1)
Answer: -3,6,17,30,45
Workings:
Substitute each value for n from 1 to 5 into the quadratic sequence to get the first 5 terms
1^2 + 6 \times 1 -10 = -3
Marks= 2
2(b)
Does the number 765 appear in this sequence?
ANSWER: Multiple Choice (Type 1)
A: Yes
B: No
Answer: A
Workings:
765 is the 25^{th} term in the sequence
Marks= 1
Question 3
The n^{th} term following quadratic sequences can be expressed in the form an^2 + bn + c. Give the values of a, b and c
3(a)
14, 20, 28, 38, 50ANSWER: Multiple Answers (Type 1)
Answer: a=1, b=3, c=10
Workings:
2^{nd}difference=2
2a=2
a=1
1^{st}difference=6
3a+b=6
b=3
a+b+c=first term
1+3+c=14
c=10
n^{th}term is n^2+3n+10
Marks=3
3(b)
0, 0, 2, 6, 12ANSWER: Multiple Answers (Type 1)
Answer: a=1, b=-3, c=2
Workings:
2^{nd}difference =2
2a = 2
a=1
1^{st}difference=0
3a+b = 0
3 \times 1 + b = 0
b=-3
a+b+c=0
1-3+c=0
c=2
n^{th}term is n^2-3n+2
Marks= 3
3(c)
4, 5, 8, 13, 20ANSWER: Multiple Answers (Type 1)
Answer: a=1, b=-2, c=5
Workings:
2^{nd} difference= 2
2a=2
a=1
1^{st}difference=1
3a+b= 1
3 \times 1+b=1
b=-2
a+b+c=4
1-2+c=4
c=5
n^{th}term is n^2-2n+5
Marks=3
3(d)
100, 96, 90, 82, 72ANSWER: Multiple Answers (Type 1)
Answer: a=-1, b=-3, c=102
Workings:
2^{nd}difference=-2
2a=-2
a=-1
1^{st}difference=-4
3a+b=-4
3 \times -1 + b=-4
b=-3
a+b+c=100
1-3+c=100
c=102
n^{th}term is-n^2-3n+102
Marks= 3
Question 4
Find the n^{th} term for the following sequences
4(a):
2, 6, 12, 20, 30ANSWER: Multiple Answers (Type 1)
Answer: a=1, b=1, c=0
Workings:
2^{nd}difference=2
a=1
1^{st}difference=4
3a+b=4
b=1
a+b+c=2
c=0
n^{th}term is n^2+n
Marks=3
4(b):
3, 10, 21, 36, 55ANSWER: Multiple Answers (Type 1)
Answer: a=2, b=1, c=0
Workings:
2^{nd}difference=4
a=2
1^{st}difference=7
3a+b=7
b=1
a+b+c=3
c=0
n^{th}term is 2n^2+n
Marks= 3
4(c):
0, 5, 12, 21, 32ANSWER: Multiple Answers (Type 1)
Answer: a=1, b=2 c=-3
Workings:
2^{nd}difference=2
a=1
1^{st}difference=5
3a+b=5
b=2
a+b+c=0
c=-3
n^{th}term is n^2+2n-3
Marks= 3
4(d):
1, 9, 19, 31, 45ANSWER: Multiple Answers (Type 1)
Answer: a=1, b=5 c=-5
Workings:
2^{nd}difference=2
a=1
1^{st}difference=8
3a+b=8
b=5
a+b+c=1
c=-5
n^{th}term is n^2+5n-5
Marks=3
Question 5
A quadratic sequence is shown below.
x, (x+y), (x+y+4), (x+y+10)The sequence has an n^{th} term of n^2-n+5
Find the values of x and y.
ANSWER: Multiple Answers (Type 1)
Answer: x=5 & y=2
Workings:
When n=1
1^2-1+5=x
x=5
When n=2
2^2-2+5=(x+y)
2^2-2+5=(1+y)
y=2
Marks=2