a/b , ab , a−b , a+b
Above shows real numbers that belong to an arithmetic progression in order. Find the next term of this sequence.
In the question I was able to come up with different answers like find d and using formula of of a + (n-1)*d Then another answer is 2(a+b) = a-b + variable
But I guess there needs to be a term which is simple Got any Ideas?
Since they belong to an AP, then suppose the first term of the AP is given by $A$ and the common difference is $d$. Thus, we have the following equations:
$$ a/b = A \\ ab = A + d \\ a - b = A + 2d \\ a + b = A + 3d \\ $$
Solving the above system yields: $ a = -9/8, b = -3/5, A = 15/8, d = -6/5$.
Thus, the next term would be $A + 4d = \boxed{-\frac{117}{40}}$