Question

What number would come next in the sequence? 3,11,19,27,35,

Answer 1

what number would come next in the sequence? 3,11,19,27,35

we have

a1=3

a2=11

a3=19

a4=27

a5=35

so

a2-a1=111-3=8

a3-a2=19-11=8

a4-a3=27-19=8

a5-a4=35-27=8

This is an arithmetic sequence and the common difference d is equal to 8

the next term is

a6=a5+d

a6=35+8=43

answer is 43

Part 2

if Victoria were to put in his school at(0;0) on a coordinate plane her house house would be located at(6,8) if each unit is equal to half of a mile how many miles away from is Victoria house?

Find out the distance

The formula to calculate the distance between two points is equal to

`d=\sqrt[]{(y2-y1)^2+(x2-x1)^2}`

substitute the given values

`\begin{gathered} d=\sqrt[]{(8-0)^2+(6-0)^2} \\ d=\sqrt[]{64+36} \\ d=\sqrt[]{100} \\ d=10\text{ units} \end{gathered}`

Remember that

each unit is equal to half of a mile

so

10(1/2)=5 miles

the answer is 5 miles