Question
The table shows some information about two sequences.
(a) Complete the table.
(b) Find the smallest positive number in sequence B.
▶️Answer/Explanation
(a)40, –275
(b) $24$
(a) To get the 5th term put $n=5$ in both sequence.
sequence A = $60 -4n=60-20=40$
sequence B= $n^2 -300=(5)^2-300=-275$
(b)
$
B = n^2 – 300
$
For the smallest positive number
$
n^2 – 300 > 0 \implies n^2 > 300
$
$
n > \sqrt{300} \approx 17.32
$
Since n must be an integer, the smallest value of n is 18.
$
B = 18^2 – 300 = 324 – 300 = 24
$
Question
These are the first five terms of a sequence
$11 \quad \quad 18 \quad \quad 25 \quad \quad 32 \quad \quad 39$
Find an expression for the $n$th term of the sequence.
▶️Answer/Explanation
$7n+4$
$
11, 18, 25, 32, 39
$
the difference between consecutive terms
\( 18 – 11 = 7 \)
\( 25 – 18 = 7 \)
\( 32 – 25 = 7 \)
\( 39 – 32 = 7 \)
The common difference is 7.
The formula for the \( n \)th term of an arithmetic sequence is
$
a_n = a_1 + (n – 1)d
$
Where
\( a_1 \) is the first term (\( 11 \))
\( d \) is the common difference (\( 7 \))
$
a_n = 11 + (n – 1)(7)
$
$
a_n = 11 + 7n – 7
$
$
a_n = 7n + 4
$
Question
The nth term of a sequence is \(an^2 + bn\).
(a) Write down an expression, in terms of a and b, for the 3rd term.
(b) The 3rd term of this sequence is 21 and the 6th term is 96.
Find the value of a and the value of b.
You must show all your working.
a = ……………………
b = ……………………
Answer/Explanation
Ans:
(a) 9a + 3b
(b) 36a + 6b = 96 or 9a + 3b = 21
for correct method to eliminate one variable
a = 3
b = -2
Question
Find the nth term in each of the following sequences.
(a) \(\frac{1}{3}\). \(\frac{2}{4}\), \(\frac{3}{5}\), \(\frac{4}{6}\), \(\frac{5}{7}\),
(b) 0, 3, 8, 15, 24, ……
Answer/Explanation
Ans:
(a) \(\frac{n}{n + 2}\) oe final answer
(b) \(n^2-1\) oe final answer
Question
7, 5, 3, 1, – 1, …
(a) Find the next term in this sequence.
(b) Find the nth term of the sequence.
Answer/Explanation
Ans:
(a) -3
(b) 9 – 2n oe