Page 217 - Math Smart - 7

Because the common difference is 5, we compare the given sequence to
-2^ the multiples of 5.

Position in the sequence, n 1 2 3 4 5
Terms 1 6 11 16 21
Multiples of 5 5 10 15 20 25

5-4 10-4 15-4 20-4 25-4
(Multiples of 5) -4
= 1 = 6 = 11 = 16 = 21

So, each term in the given sequence = multiples of 5 - 4.
Ti = 1= 5-4 = 5x1-4
12 = 6 = 10-4 = 5x2-4
T3 = 11 = 15-4 = 5 X 3-4

14=16 = 20-4 = 5x4-4
T5 = 21 =25-4 = 5 X 5-4
So, Tn = 5 X /? - 4 = 5// - 4.

Check My
Understanding

For each of the following sequences,
O "find a formula for the general term of the sequence, Tn.
© determine the 100'^ term.
a) 10, 12, 14,16,... b) 9,14,19,24,... c) 16,20,24,28,
d) 13,24,35,46,... e) 3,7,11,15,... f) 2,6,10,14,...
g) 5,9, 13, 17, ... h) 7, 12, 17,22, ... i) 2,8,14,20,...

Investigate!

Find out what palindrome numbers are on the Internet.
Then investigate the pattern found in palindromic numbers.

a) Use a calculator to find all the palindromic multiples of 13 that are less
than 1000.
b) Describe the pattern in these numbers.