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Question
The sum of terms equidistant from the beginning and end in an A.P. is equal to ______.
Solution
The sum of terms equidistant from the beginning and end in an A.P. is equal to the [first term + last term].
Explanation:
Let A.P be a, a + d, a + 2d, a + 3d, …, a + (n – 1)d
Taking first and last term
a1 + an = a + a + (n – 1)d
= 2a + (n – 1)d
Taking second and second last term
a2 + an–1 = (a + d) + [a + (n – 2)d]
= 2a + (n – 1)d = a1 + an
Taking third from the beginning and the third from the end
a3 + an–2 = (a + 2d) + [a + (n – 3)d]
= 2a + (n – 1)d
= a1 + an
From the above pattern, we observe that the sum of terms equidistant from the beginning and the end in an A.P is equal to the [first term + last term]
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