GIVE THE PATTERN RULE OF THE SEQUENCE WORKSHEET

Part A

Write down the first five terms of the sequence given by

(1)  u_n  =  2n - 1

(2)  u_n  =  2n + 5

(3)  u_n  =  2n + 5

(4)  u_n  =  7n + 2

(5)  u_n  =  - 2n + 5

(6)  u_n  =  - 3n + 4            Solution

7)  A sequence has first term 20 and the difference between the terms is always 31.

a) Determine a formula to generate the terms of the sequence

b)  Calculate the first 5 terms of the sequence.

8)  The second and third terms of the sequence are 16 and 27. The difference between successive terms in the sequence is always constant.

a)  Determine the general formula of the sequence.

b)  Calculate the first 5 terms of the sequence.

Part B

Use the rules to list the first six terms of the sequence 

(1)  Start with 1 and add 2 each time

(2)  Start with 3 and multiply by 2 each time

(3)  Start with 24 and subtract 8 each time

(4)  Start with 32 and divide by 2 each time

(5)  start with 5 and double each time

(6)  Start with 1 and 2 and add the previous two numbers to get the next one.

7)  For the sequence 

6, 12, 24, 48, 96, ............

a) Calculate the next 2 terms of the sequence.

b)  Determine the general formula for nth term.

8)  Calculate the next three terms of the sequence.

1, 4, 16, 64, 256

i) Determine the formula for the nth term of the sequence.

9)  Determine the formula for the general term of each of the following sequences :

i)  15, 75, 375, 1875, 9375,.............

ii)  1, 3, 9, 27, 81, ............

iii)  20, 200, 2000, 20000, .........

iv)  4, 28, 196, 1372, 9604, .............

10)  A plant that is 17 cm tall grows 2 cm each week.

a) Continue the sequence

17, ___, _____, _____

1 week, 2 weeks, 3 weeks

b) How tall will the plant be after three weeks ?

c) After how many weeks will the plant be 27 cm tall?

11)  Make a pattern to solve the problem.

a) Hanna has $49. She spends $8 each day. How much money does she have left after 5 days ?

b) Matt has roll of 74 stamps. He uses 7 stamps each day for 4 days. How many stamps are left ?

Solution

Part C

Find the rule which will generate the sequence :

1)  4, 7, 10, 13, 16, ……

2)  - 2, 3, 8, 13, 18, ……

3)  1, 7, 13, 19, 25, ……

4)  3,  10,  17,  24,  31, ……

5)  40,  37,  34,  31, ……

6)  76, 72, 68, 64, ……

7)  8, 3, -2, -7, ……

8)  127, 121, 115, 109, ……

9)  1/3,  2/5,  3/7,  4/9,  5/11 ……

Solution

10)  Four sequences A, B, C and D are defined by the following formulae

A : U_n = 8n + 2

B : U_n = 7n - 3

C : U_n = 3n + 1

D : U_n = 100 - 6n

a)  Which sequence have 4 as their first term ?

b)  Which sequence is decreasing ?

c) Which sequence has a difference of 7 between terms ?

d) Which sequence has 301 as its 100^th term ?

Solution

11)  Look at the part of the number line, write down the 2 missing numbers.

Copy and complete the sentence

The numbers on this line go up in steps of _______

Solution

12)  Jeff makes a sequence of patterns with black and grey triangular tiles.

The rule of finding the number of tiles pattern number N in Jeff's sequence is

Number of tiles = 1 + 3N

i)  The 1 in this rule represents the black tile. What does the 3N represent ?

ii)  Jeff makes pattern number 12 in this sequence. How many black tiles and how many grey tiles does he use ?

iii)  Jeff uses 61 tiles altogether to make a pattern in his sequence, what is the number of pattern he makes ?

Solution

1)  added by +3

2)  added by +5

3) added by +6

4)  added by +7

5)  subtracted by -3

6)  subtracted by -4

7)  subtracted by -5

8)  subtracted by -6

9)  So, the rule is n/(2n+1)

10) a)  U₁ = 4   b)  sequence D is the decreasing sequence.

c)  in sequence B the difference between two terms is 7

d)  100th term of sequence C is 301.

11)  Then the missing terms are -3 and 14.

12)    12th pattern number of black tiles is 1 and number of grey tiles = 36.

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