Any term of an A.P. (except the first) is equal to half the sum of terms which are equidistant from it.

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alok kumar singh | Contributor-Level 10

4 months ago

This is a True or False Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} L e t u s c o n s i d e r a A . P, a, a + d, a + 2 d, \dots \\ ∴ a_{2} + a_{4} = a + d + a + 3 d = 2 a + 4 d = 2 a_{3} \\ \Rightarrow a_{3} = \frac{a_{2} + a_{4}}{2} \\ \frac{a_{2} + a_{4}}{2} = \frac{a + 2 d + a + 4 d}{2} = \frac{2 a + 6 d}{2} = a + 3 d = a_{4} \\ H e n c e, t h e g i v e n s t a t e m e n t i s T r u e . \end{array}$

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Any term of an A.P. (except the first) is equal to half the sum of terms which are equidistant from it.

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