Find the sum of ( m − n ) t h and ( m + n ) t h terms if m t h is 5 .
D e t a i l s :
All terms are terms of an A.P.
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This is such a troll question! :D
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OVERRATED ._.
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Yes, you are right math man.. I was shocked when I saw that it is for 125 points.
Solving is our tasks.
The series is A.P & its m t h term is 5.
Let's think of a simplest series having these properties: 5 , 5 , 5 , 5 , . . . . . Now we can give values to m & n as we please without breaking any order. Let m = 3 , n = 1 Now one can get the answer which is 5 + 5 = 1 0 .
This simple method of arriving at the answer very fast is totally logical . Such methods are appropriate only when they are not breaking the guidelines of logic.
such methods are really useful for functions,, when a particular property of some function is given,, while the actual or most general solutions involve not assuming the function as any known function and directly using the property given in question,, it is often convenient to compare it and find some known function that satisfies the property and thus easily get answer,, especially for objective questions :)
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If m th term is 5 , m − n th term is 5 − n d if d is the difference. m + n th term is also 5 + n d .
Therefore, the sum = 5 − n d + 5 + n d = 1 0 . No matter what the difference is, they cancel out. ~~~