Two arithmetic progressions have the same numbers. The reatio of the last term of the first progression to the first term of the second progression is equal to the ratio of the last term of the second progression to the first term of first progression is equal to 4. The ratio of the sum of the n terms of the first progression to the sum of the n terms of teh first progression to the sum of the n terms of the second progerssion is equal to 2.
The ratio of their first term is

Options

A. G.M of a and b is 3
B. one possible value of a + 2b is 11
C. A.M of a and b is 6
D. greatest value of a-b is 8

Answer

A, B, D

Explanation

`x+y+z=3((a+b)/2)`
`rArr15-3((a+b))/2`
`rArra+b=10`
`1/x+1/y+1/z=(3(1/a+1/b))/2`
`rArr5/3=(3(a+b))/(2ab)=(3xx10)/(2ab)`
`rArrab=9` (2)
From (1) and (2), a=9,b=1 or a=1 and b=9. Hence, G.M.
`=sqrt(ab)=3,a+2b=11` or 19.