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

Answer

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

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