The first three patterns in a sequence are shown - Junior Cycle Mathematics - Question 6 - 2019
Question 6
The first three patterns in a sequence are shown.
(a) Draw Pattern 6 in the sequence.
(b) Fill in the table to show the number of small squares in each of the firs... show full transcript
Worked Solution & Example Answer:The first three patterns in a sequence are shown - Junior Cycle Mathematics - Question 6 - 2019
Step 1
Draw Pattern 6 in the sequence.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To draw Pattern 6, observe the given patterns and identify the growth. Based on the pattern structure, create a visual representation of Pattern 6, which should depict 6 rows of squares, extending the sequence from previous patterns.
Step 2
Fill in the table to show the number of small squares.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The completed table of small squares should show:
Pattern
Number of small squares
1
2
2
5
3
10
4
17
Step 3
The number of small squares in Pattern 20.
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Using the formula (n^{2} + 1) where (n = 20), we substitute to find the number of small squares:
[20^{2} + 1 = 400 + 1 = 401]
Thus, the number of small squares in Pattern 20 is 401.
Step 4
What kind of sequence is made by the number of small squares in each pattern?
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The sequence is quadratic. This is evident from the formula (n^{2} + 1), where the square of the term identifies it as quadratic. The consistent second difference also supports this classification.
Join the Junior Cycle students using SimpleStudy...
