Question

Directions: Find the next three terms (1 point term) in each sequence.
Then, write the rule for finding the nth term (2 points).
1.1, 4, 9, 16,
Rule:
2. 3, 5, 7, 9,
Rule:
3. 20, 16, 12, 8,
Rule:​

Answer 1

Directions: Find the next three terms (1 point term) in each sequence.

Then, write the rule for finding the nth term (2 points).

1.1, 4, 9, 16,

Rule:

2. 3, 5, 7, 9,

Rule:

3. 20, 16, 12, 8,

Rule:

Answer 2

Answer:

as given below

Step-by-step explanation:

Given problem  

Find the next three terms in each sequence.

Then, write the rule for finding the nth term    

1. 1, 4, 9, 16,

⇒  1, 4, 9, 16  =   1² 2² 3³    

⇒ next 3 terms = 4², 5² , 6² =  16, 25, 36

⇒ number sequence = 1 , 4, 9, 16, 25, 36...

Rule for finding nth term: n²  

2. 3, 5, 7, 9

⇒ each value in above sequence is  

   3 = 2(1) + 1 = 3

   5 = 2(2) + 1 = 5

   7 = 2(3) + 1 = 7

   9 = 2(4) + 1 = 9

⇒ next three terms  ⇒ 2(5) +1 = 10 + 1 = 11

                                     2(6) + 1 = 12 + 1 = 13

                                     2(7) + 1 = 14 + 1 = 15  

⇒ the number sequence is 3, 5, 7, 9, 11, 13, 15 ...

Rule for finding nth term: 2n + 1

3. 20, 16, 12, 8

⇒ each value in above sequence is  

    20 - 4 = 16 =   [20 - 1(4) ]      

    16 - 4 = 12  =   [20 - 2(4)]

    12 - 4 = 8    =  [20 -  3(4)]        

⇒ next 3 terms  ⇒  8 - 4 = 4  

                                4 - 4 = 0

                                0 - 4 = - 4  

⇒ number sequence = 20, 16, 12, 8, 4, 0, -4  

Rule for finding nth term: (20 - 4n)