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how to solve this question? Please tell the solution of this question.I am not understanding how to solve this.

how to solve this question? Please tell the solution of this question.I am not understanding how to solve this.

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Grade:12

1 Answers

mycroft holmes
272 Points
7 years ago
Let the first term be a and common difference = d. 
The given relation yields a+5d = 3......1
 
Since a is not an integer, d cannot be an integer, but its rational
 
Let the fractional part of a be f0 and that of d be f1.
 
Since every alternate term is an integer, this means 2f1 is an integer. Hence f1= ½ 
 
From eqn 1, its now clear that f0 = ½ 
 
So let a = m+ ½ and d = n + ½ with m>0
 
So from Eqn 1, we get m+5n = 0. So, possible pairs of m, n are (5,-1), (10,-2), (15,-3) etc. and correspondingly (a,d) can be (11/2, -1/2), (21/2, -3/2), (31/2, -5/2) and so on.
 
So possible choices for 3rd term are 4,6,8...
 
Of the given alternatives, Option (D) i.e. 6 is the answer.

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