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  • State whether statement in True or False. Any term of an A.P. (except first) is equal to half the sum of terms which are equidistant from it.

State whether statement in True or False.

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

Answers (1)

Let us consider an A.P a, a+d, a+2d, a+3d

\\a_{2}+a_{4}= \left( a+d \right) + \left( a+3d \right) =2 \left( a+2d \right) =2 \left( a_{3} \right) ~~~~ \\\\ ~a_{3}=\frac{a_{2}+a_{4}}{2}~ \\\\

Hence, the given statement is TRUE.   

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infoexpert21

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