Q32 of 36 Page 161

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.


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

∴ a2 + a4 = a + d + a + 3d


= 2a + 4d


= 2(a + 2d)


a2 + a4 = 2a3


[∵a3 = a + (3 – 1)d = a + 2d]



∴ the third term is equal to half the sum of the second and fourth term.


Hence, the given statement is TRUE


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