1) Write an expression to represent the pattern. 19, 27, 35, 43 ...

2) Write an expression to represent the sequence. 71, 62, 53, 44 ...

1) The expression to represent the pattern is 11 + 8n

2) The expression to represent the pattern is 80 - 9n

Step-by-step 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