Arithmetic sequences

Solve the inequality with the natural variable $x$: $$\sum _{n=1}^x(5-\frac{1}{2}n)\ge x$$

Suppose three numbers form three consecutive terms of an arithmetic sequence. The sum of these numbers is $36$ and the product is $-972$. Find the biggest of these three numbers.

Insert $3$ numbers between the roots of the equation $5x^2-26x+5=0$ such that the resulting sequence is a part ($5$ terms) of an increasing arithmetic sequence with the common difference $d$. Choose the incorrect statement about the common difference $d$.

The picture shows a part of the graph of the arithmetic sequence. Find the sum of the first twenty-four terms of the sequence.