You will need

- An arithmetic progression

Instruction

1

An arithmetic progression is a sequence of numbers a1, a1+d, a1+2d,..., a1+(n-1)d. The number d is called the step

**progression**.It is obvious that the General formula for arbitrary n-th term of the arithmetic**progression**has the form: An = A1+(n-1)d. Then knowing one of the members**of the progression**, the first term**of the progression**and step -**progression**, you can determine that is the number of member progression. Obviously, it will be determined by the formula n = (An-A1+d)/d.2

Now suppose the known m-th member

**of progression**and some other member of the**progression**is n, but n is unknown, as in the previous case, but we know that n and m do not coincide.Step**progression**can be calculated according to the formula: d = (An-Am)/(n-m). Then n = (An-Am+md)/d.3

If we know the sum of several elements of the arithmetic

**progression**, and its first and last element, the number of these elements can also be determined.Sum of arithmetic**progression**is equal to: S = ((A1+An)/2)n. Then n = 2S/(A1+An) the number Chudinov**progression**. Using the fact that An = A1+(n-1)d this formula can be rewritten in the form: n = 2S/(2A1+(n-1)d). From this formula we can Express n by solving the quadratic equation.