Question

please give me full solution

Answer 1

Note: The first three terms can be anything. It can be a-d,a,a+d.

I am assuming the first three terms as a,a+d,a+2d.

Given that sum of the first three terms of an AP is 48.

a + a + d + a + 2d = 48

3a + 3d = 48

a + d = 16   --------------------- (1)


Given that the product of 1st and 2nd terms exceeds 4 times the 3rd term by 12.

a * (a + d) = 4 * (a + 2d) + 12

a * 16 = 4a + 8d + 12

16a = 4a + 8d + 12

12a - 8d = 12   --------------- (2)

On solving (1) * 12 & (2), we get

12a + 12d = 192

12a - 8d = 12

---------------------

20d = 180

d = 9.


Substitute d = 45 in (1), we get

a + d = 16

a + 9 = 16

a = 16 - 9

a = 7.


Therefore the AP is 7,16,25...



Hope this helps!