Question

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

Answer 1

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