Question

Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 2, , 10, , 18, , . 2,10,18,...This is

sequence and the
is equal to ?

Answer 1

Answer: arithmetic, common difference = 8

Step-by-step explanation

The sequence is not geometric because dividing each term by its previous term gets us different results

• r = term2/term1 = 10/2 = 5
• r = term3/term2 = 18/10 = 1.8

But the sequence is arithmetic because subtracting adjacent terms gets us the same result (the common difference 8)

• d = term2 - term1 = 10 - 2 = 8
• d = term3 - term2 = 18 - 10 = 8

It means that we add 8 to each term to get the next term.

• 2+8 = 10
• 10+8 = 18

and so on.