Why do we take the first four consecutive terms of an A.P. as a-3d, a-d, a+d, a +3d and not as a-d, a, a+d, a+2d?(I tried a question and we get the answer only if we take a-3d, a-d, a+d, a +3d as the terms.)
Answers
#BAL
The standard form of an A.P. is
a, a+d, a+2d, a+3d,……….
in which the first term is a, and the common difference is d. This form is invariably used in problems relating to A.P. There are however some special situations when we write the terms as a-d, a, a+d. One such instance is in finding the arithmetic mean of three quantities. You can at once see that a [=(a-d+a+a+d)/3] is the mean.
Another instance is when solving a problem. Suppose you are given the sum of three numbers in A.P. as 27 and the sum of their squares as 293. You are asked to find the numbers. If you take a as the middle number, d the common difference, then the three numbers are taken as a-d, a, a+d and their sum simplifies to a-d+a+a+d = 3a = 27 whence a=9. Once one number is known, d can be found from using the second condition and then all the three numbers.
You can see from the above two examples that by writing the three quantities in the form a-d, a, a+d the algebra is simplified.
As in AP the common difference should remain same.
Difference between a+d-a+d=2d
Whereas a-d-a+2d=d
Hence this is not an AP.
So a-3d,a-d,a+d,a+3d are taken
Bro look at that okay
If took terms as a+d, a-d,a+3d,a-3d..
we can see the difference between terms is 2 which refer even no and easy to solve.. Thereforw its given in ques 4consecutive terms 4 is even therefore we have taken this .
In case we take second one it is refer for ols no.s case e.g., If there three consecutive no.s in question
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