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In an arithmetic progression, sum of terms equidistant from the beginning and the end is equal to the:

In an arithmetic progression, sum of terms equidistant from the beginning and the end is equal to the: Correct Answer Sum of the first and the last term.

Concept:

Arithmetic Progression (AP): The series of numbers where the difference of any two consecutive terms is the same, is called an Arithmetic Progression.

An Arithmetic Progression of n terms with first term a and common difference d is represented as:

a, a + d, a + 2d, a + 3d, ..., a + (n - 2)d, a + (n - 1)d.

 

Calculation:

Let the Arithmetic Progression consisting of n terms, with first term a and common difference d, be:

a, a + d, a + 2d, a + 3d, ..., a + (n - 2)d, a + (n - 1)d.

Sum of first term and last term = a + a + (n - 1)d = 2a + nd - d.

Sum of second term and second last term = a + d + a + (n - 2)d = 2a + nd - d.

And so on.

So, we can say that in an Arithmetic Progression, the sum of the terms equidistant from the beginning and the end is equal to the sum of the first and the last term.

Related Questions

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