Answer:

Step-by-step explanation:
<u>The correct question is:</u> 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;
![S_n = \frac{n}{2}[\text{first term} + \text{last term}]](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%5B%5Ctext%7Bfirst%20term%7D%20%2B%20%5Ctext%7Blast%20term%7D%5D)
{using equation 1}
![S_n = \frac{b}{2 (b-a)}[3a]](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bb%7D%7B2%20%28b-a%29%7D%5B3a%5D)

Hence proved.