Question

If the sum of 3 number in



a.P is 45 and product is 3135 .Find common different

Answer 1

Here is your answer buddy,

Let the numbers be a−d, a and a+d, clearly d is the common difference.

Now,

The 3 numbers are in AP.

Therefore,

By adding up three numbers we get,

a-d+a+a+d = 45
=> 3a = 45 ( d and d get cancelled)
=> a = 15 ---------(1)

Again,

By multiplying the three numbers we get,

(a-d)×a×(a+d) = 31315
=> {$a^{2} - ad$}×(a+d) =3135
=> $a^{3} - a^{2}d + a^{2}d - ad^{2}$ =3135
=> $15^{3} - 15^{2}d + 15^{2}d - 15d^{2}$ =3135
(from 1)
=> 3375 - 225d + 225d - 15d = 3135
=> 3375 - 15d = 3135
(225d and 225 d get cancelled)
=> - 15d = 3135 - 3375
=> - 15d = - 240
=> d = 16 (minus got cancelled)

So the common difference is 16.

Hope this helps you.
Be Brainly.