What is the 25th term of the sequence?

Question

X: 1, 2, 3, 4, 25

Y: -5, -1, 3, 7, ?

Answer 1

this is an arithmetic sequence problem

-5,-1,3,7,...

a₂₅=-5+(25-1)4 (look at the other problem that I did)

a₂₅=-5+24*4

a₂₅=-5+96

a₂₅=91

Answer 2

If we change the values into ordered pairs, we get (1,-5),(2,-1),(3,3),(4,7). We are trying to find the Y value for the ordered pair of (25,Y). This is going to be a linear equation, so we just need to find the slope of the line. We do this by using the equation(Y2-Y1)/(X2-X1). Lets use the first two points. (1,-5) and (2,-1).

(-5 - (-1)) / (1-2) = (-4)/(-1) = 4. We know the slope of this line is 4.

Multiply the X value in any of your points by 4, I'll take (1,-5) because its the easiest (any point will work). 1 * 4 = 4, and now we need to subtract 9 to get the Y value of -5. If you were to graph this equation, the Y intercept would be -9.

An easier way to see this equation is: Y = 4X - 9.

To find the 25th term, just plug in 25 for X. Y = 4(25) - 9, making the 25th term in this sequence 91.