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Question
Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.
Options
True
False
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Solution
This statement is True.
Explanation:
Let us consider an A.P a, a + d, a + 2d, …
∴ a2 + a4 = a + d + a + 3d
= 2a + 4d
= 2a3
⇒ a3 = `(a_2 + a_4)/2`
`(a_3 + a_5)/2 = (a + 2d + a + 4d)/2`
= `(2a + 6d)/2`
⇒ a + 3d
= a4
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