10. The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.
Let three terms of GP be
Then, we have
...............................................1
from an AP.
....................................................................2
From equation 1 and 2, we get
If r=2, GP = 8,16,32
If r=0.2, GP= 32,16,8.
Thus, the numbers required are 8,16,32.