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Math & Statistics

Arithmetic Progression Solver

Solve for the nth term and the sum of the first n terms of an arithmetic progression (AP).

Inputs

-10,00,00010,00,000
-10,00,00010,00,000
110,00,000

Calculation Results

Nth Term (a_n)

29

Sum of n Terms (S_n)

155

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Formula & Mathematical Explanation

an=a+(n−1)d,Sn=n2[2a+(n−1)d]\displaystyle a_n = a + (n-1)d, \quad S_n = \frac{n}{2} [2a + (n-1)d]

An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. The nth term (a_n) is found by adding (n-1) times the difference (d) to the first term (a). The sum (S_n) is the average of the first and last terms multiplied by the number of terms.

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