If a, b,and 2a in ap show that 3ab/2(b-a)

Step-by-step explanation:

The correct question is: If the first, second and last term of an AP are a,b and 2a respectively, then show that the sum of all terms of an AP is 3ab/2(b-a).

Firstly, as we know that the nth term of an A.P. is given by the following formula;

,  where a = first term of AP, d = common difference, n = number of terms in an AP and = last term

Since it is given that the first, second and last term of an AP are a,b and 2a respectively, that means;

first term = a

d = second term - first term = b - a

= 2a

So,  

             ------------- [equation 1]

Now, the formula for the sum to n terms of an AP when the last term is given to us is;

                   {using equation 1}

Hence proved.

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step-by-step explanation: