Q1.
Mathematical Fluency - Algebra
Nth Term of a Quadratic Sequence
Find the nth term of each of the following sequences
(a) 10, 17, 26, 37, 50,…
(b) -4, 2, 10, 20, 32,...
(d) 6, 6, 8, 12, 18,...
(e) 8, 9, 8, 5, 0,...
(g) 1, -1, 1, 7, 17,...
(h) -9, -13, -21, -33, -49,...
(j) 3, 11, 25, 45, 71,...
(k) -16, -4, 16, 44, 80,...
@MrBenHamilton
(c)
(f)
(i)
(l)
13, 21, 33, 49, 69,...
3, 17, 35, 57, 83,...
-12, -18, -26, -36, -48,...
20, 32, 36, 32, 20,...
Q2.
Calculate the 50th term of the sequences labelled (a)-(l).
Q3.
A quadratic sequence has the nth term: n2 + n + 4. Find the term that has a value of 136.
Q4.
Work out at which term the two sequences will be equal.
(Sequence a)
-2, 11, 30, 55, 86,...
(Sequence b)
12, 23, 40, 63, 92,...
At which term will sequence ‘z’ be greater than sequence ‘y’?
(Sequence y)
-1, 7, 19, 35, 55, 79,...
(Sequence z)
-19, -13, -1, 17, 41,...
Q5.
Q6.
Show that the nth term
of the pattern is:
Bonus Question!
What is this birds favourite math topic?
Q1.
(a) n2 + 4n + 5
(e) -n2 + 4n + 5
(i) -n2 – 3n – 8
Mathematical Fluency - Algebra
Nth Term of a Quadratic Sequence
Answers:
(b) n2 + 3n – 8
(c) 2n2 + 2n + 9
(f) 2n2 + 8n – 7
(g) 2n2 – 8n – 7
(j) 3n2 – n + 1
(k) 5n2 – 20
Q2.
(a) 2705
(e) -2245
(i) -2658
(b) 2642
(f) 5393
(j) 7451
Q3.
Q4.
Q5.
Q6.
n2 + n + 4 = 136
3n2 + 4n – 9 = 3n2 + 2n + 7
3n2 – 3n – 19 > 2n2 + 2n – 5
(c) 5109
(g) 4607
(k) 12480
n2 + n – 132 = 0
2n = 16
n2 – 5n – 14 > 0
@MrBenHamilton
(d) n2 – 3n + 8
(h) -2n2 + 2n – 9
(l) -4n2 + 24n
(d) 2358
(h) -4909
(l) -8800
(n + 12)(n – 11)
n=8
(n – 7)(n + 2)
11th Term
8th Term
8th Term
Bonus Question: Owlgebra