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
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