Question

In the following table of values, the first differences are

x y First Difference
-2 34
-1 27
0 20
1 13
2 6

Answer 1

-7

Explanation:

Given

`\begin{array}{ccc}x & {y} & {First\ difference} & {-2} & {34} & {}&{-1} & {27} & {} &{0} & {20} & {} & {1} & {13} & {} & {2} & {6} &{} \ \end{array}`

Required

The first difference

To do this, we simply calculate the difference between the consecutive y-values.

i.e.

`d = y_(n+1) - y_n`

So, we have:

`d = y_2 - y_1 = 27 - 34 = -7`

`d = y_3 - y_2 = 20 - 27 = -7`

`d = y_4 - y_3 = 13 - 20 = -7`

`d = y_5 - y_4 = 6-13 = -7`

Hence, the first differences are -7 (all through)