Question

consider the terms to be in descending order​

Answer 1

Step-by-step explanation:

Let the three terms in the AP be a-d , a and a+d

Given - Sum of consecutive terms = 36

So , (a-d) + a + (a+d) = 36

      => a - d + a + a + d = 36

      => 3a = 36

      => a = 12

Also given, Product of the terms = 1140

          => (a-d) * a * (a+d) = 1140

  putting value of a in above case

           => (12-d) * 12 * (12+d) = 1140

           => (12-d) * (12+d) = 1140 /12

           => (12-d) * (12+d) = 95

           => 12^2 - d^2 = 95     [ Using identity (a+b) * (a-b) = a^2 - b^2 ]

           => 144 -d^2  = 95

           => d^2 = 95 - 144

           => d^2 = 49  => d = 7

           So now we have a and d both

So terms = a-d = 12 - 7 = 5   ( First term )

                   a = 12 ( second term )

                 a + d = 12 + 7 = 19 ( third term )

Now we will write it in descending order as guided in question

            = 19 , 12 , 5 are the required AP

Hope this answer helps you :)