What is the 35th term of the sequence?

Question

X: 1, 2, 3, 4, 35

Y: -4, -2, 0, 2, ?

Answer 1

Let's figure out first if this is really an arithmetic sequence.

If you try to subract the first from second of any two consecutive terms and they all have the same result, then it is arithmetic.

-2-(-4) = 2

0 -(-2) = 2

2 - 0 = 2. It's arithmetic sequence and with common difference of 2 (d=2)

The explicit formula for arithmetic sequence using X and Y is:

Y(X) = Y(1) + d(X-1) where Y(1) is the first term of the sequence.

The 35th term or Y(35) is solved this way:

Y(X) = Y(1) + d(X-1)

Y(35) = -4 +2(35-1)

Y(35) = -4 +2(34)

Y(35) = -4 + 68

Y(35) = 64

Answer 2

the slope of the line is 2.

B = y - mx.

Using the first point (1,-4) ---> B = -4 - 2(1) = -6

y = 2x-6

so for x=35, y = 2(35)-6 = 70-6 = 64