Answer
1) The expression to represent the pattern is 11 + 8n
2) The expression to represent the pattern is 80 - 9n
Explanation:
1) Lets study the pattern;
- 19 , 27 , 35 , 43 , ..................
27 - 19 = 8
35 - 27 = 8
43 - 35 = 8
The difference is constant between each two consecutive terms
It is an arithmetic sequence
Lets take about the arithmetic sequence
If the first term is a and the constant difference is d
a1 = a , a2 = a + d , a3 = a + 2d , a4 = a+ 3d , ........
an = a + (n - 1)d, where n the position of the term in the sequence
Now we will use this rule to find the expression of our pattern
a = 19 , d = 8
an = 19 + (n - 1)(8) ⇒ an = 19 + 8n - 8 ⇒ an = 11 + 8n
Lets check it;
a3 = 11 + 8(3) = 11 + 24 = 35 ⇒ true
The expression to represent the pattern is 11 + 8n
Step 2) Lets study the pattern;
- 71 , 62 , 53 , 44 , ...
62 - 71 = -9
53 - 62 = -9
44 - 53 = -9
The difference is constant between each two consecutive terms
It is an arithmetic sequence
We will use the same rule above to find the expression of the pattern
a = 71 , d = -9
an = 71 + (n - 1)(-9) ⇒ an = 71 + -9n + 9 ⇒ an = 80 - 9n
Lets check it;
a4 = 80 - 9(4) = 80 - 36 = 44 ⇒ true
The expression to represent the pattern is 80 - 9n