Q. 74.3( 6 Votes )

The Sum of the three terms of an A.P. is 21 and the product of the first, and the third terms exceed the second term by 6, find three terms.

Answer :

Given: the sum of first three terms is 21


To find: the first three terms of AP


Assume the first three terms are a - d, a, a + d where a is the first term and d is the common difference


So, sum of first three terms is a - d + a + a + d = 21


3a = 21


a = 7


it is also given that product of first and third term exceeds the second by 6


so (a - d)(a + d) - a = 6


a2 - d2 - a = 6


substituting a = 7


72 - d2 - 7 = 6


d2 = 36


d = 6 or d = - 6


Hence the terms of AP are a - d, a, a + d which is 1, 7, 13 or 13, 7, 1

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