quick help!..

When x=1, y=5, when x=2, y=9, when x=3, y=13, and so on. What is the value of y, when x=10?

Solution:

We know that the difference between y and x is 4, as we can see in our pattern. But, if we look more closely, we can see that 4x+1=y. (1*4+1, 2*2+1=5, 3*4+1=13, and so on). So, to find y when x=10, we simply do 4(10)+1=\(\boxed{41}\)

There is a more reliable way to do this. 

We notice that these can be expressed as points of a line,

\((1,5);(2,9);(3,13)...\)

We can treat this as a function problem, and we need to solve for the equation of the line. 

You first find the slope. 

\(\frac{9-5}{2-1}=4\\ y=4x+b\\ 5 = 4\cdot1+b\\ b=1\)

The equation of the line is \(y=4x+1\)

Now we plug in x = 10, 

\(y = 4\cdot10+1=\boxed{41}\)

I hope this helped,

Gavin

Both x and y form an arithmetic series. Use the nth term formula to find the value of y when x = 10

nth term =F + (N - 1)*D, where F=First term, N = Number of terms, D =Common difference

10th term = 5 + (10 - 1)*4

                = 5 + (9*4)

                = 41