Question

The numbers x, y and z are the first three terms of an arithmetic sequence. Express z in terms of x and y.

Short answer

z expressed in terms of x and y is$z=2y-x$ .

Step-by-step solution

Step 1. Given Information.

Given first three terms of an arithmetic sequence are x, y, z.

Step 2. Calculation.

A sequence is said to be arithmetic when the difference between the consecutive terms is always the same.

Here the difference between the first two terms is $y-x$

The difference between the next two terms is $z-y$

So, the difference is equal.

$\begin{array}{l}z-y=y-x\\ z=y-x+y\\ z=2y-x\end{array}$

Step 3. Conclusion.

Hence, z expressed in terms of x and y is $z=2y-x$