Question

three numbers are in A.P whose sum is 21. if 2,2,14 are added to them respectively. the number are in G.P. Find the numbers

Answer 1

Answer:

Dear student,

Let the numbers in AP be a-d, a, a+d.

It is given that the sum of these numbers is 21.

So, a-d+a+a+d = 21

This gives, a = 7

So, the numbers are 7-d, 7, 7+d.

It is given that if 2, 2, 14 respectively are added to the numbers, then the resulting numbers are in GP.

So, 9-d, 9, 21+d are in GP.

Therefore,

9/9-D =21+d/9

by simplyfying this we get

d^2+12d-108=0

=(d+18)(d-6)=0

d=-18 or 6

Thus, when d = -18, the numbers are 25, 7, -11.

When d = 6, the numbers are 1, 7, 13

Step-by-step explanation: hope it helps you mark my answer as brainlist answer

Answer 2

Step-by-step explanation:

Given, a/b = c/d Read more on Sarthaks.com - https://www.sarthaks.com/148913/given-a-b-c-d-prove-that-3a-5b-3a-5b-3c-5d-3c-5d