Constant difference in arithmetic sequence

Question

3 consecutive terms in an arithmetic sequence are x, 2x+11 and 4x-3. what is the constant difference between consecutive terms in this sequence? I get x=25 but the answer is 36 and I am at a loss

Answer 1

The exercise is asking to find the common difference, not just $x$. Try plugging $x$ back into an equation and solve for $d$:

$$x + d = 2x + 11 \implies 25 + d = 50 + 11 \implies d = 36$$

Answer 2

In an arithmetic sequence, the difference between the terms is a constant: $d$.

So, we have $x,\ 2x+11,\ 4x-3$ as some terms in our sequence. Their differences must be equal, so we can set up some equations:

$(2x+11) - (x) = d$ --> $x+11 = d$
$(4x-3) - (2x+11) = d$ --> $2x-14 = d$

We can set the resultant equations equal to each other to solve for x:

$x+11=2x-14$ --> $25 = x$

We know $x+11 = d$, so $d=11+25 = 36$.

Ta-da!