Number Patterns

Question 1

For each of the following sequences, state the rule of the sequence and write down the next two terms.
(a) 42, 39, 36, 33, 30, …
(b) -22, -18, -14, -10, -6, …
(c) 256, 128, 64, 32, 16, …
(d) -1, 1, -1, 1, -1, …

Answer 1

(a) -3 from each term to get to the next term. the next two terms are 27 and 24
(b) add 4 to each term to get the next term. the next two terms are -2 and 2
(c) divide each term by 2 to get the next term. the next two terms are 8 and 4
(d) multiply each term by -1 to get the next term. the next two terms are 1 and -1

Question 2

Given that the nth term, Tn of a sequence is Tn = 5n - 3, find
(i) the 3rd term
(ii) the difference between the 3rd term and the 5th term of the sequence

Answer 2

(i) T3 = 5(3) - 3 = 12
(ii) T5 = 5(5) - 3 = 22
Difference between the 3rd and 5th term of the sequence = T5 - T3 = 10

Question 3

Find a formula for the general term of the sequence 7, 11, 15, 19, 23

Answer 3

Since common difference is 4, Tn = 4n + ?
The term before T1 is c = T0 = 7-4 =3

∴ general term of the sequence is Tn = 4n + 3

Question 4

Answer 4