Describe a rule for each pattern. 35,70,105,140

A linear sequence

Step-by-step explanation:

In this sequence, the difference between the first two terms is  70−35=35 , we can check this is correct by finding the difference between the 2nd and 3rd terms, which is  105−70=35 . This means the first difference is 35.

The first difference gives us the number we multiply  n  by, or the quotient of n.

This means we get the nth term as  35n+c .

To get  c , we check the difference between the first term and the number we get when we multiply  n  by  35 , when  n=1 .

This gives us:

35n+c=35  

c=35−35n  

c=35−35(1)  

c=35−35  

c=0  

Once we have  c , we get the nth term of  35,70,105  to be  35n .