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Which of the following can be terms (not necessarily consecutive) ofany A.P.?a. 1,6,19b. `sqrt(2),sqrt(50),sqrt(98)`c. `log2,log16 ,log128`d. `sqrt(2),sqrt(3),sqrt(7)`A. 1,6,19B. `sqrt(2).sqrt(50),sqrt(98)`C. log 2,log 16 , log128D. `sqrt(2),sqrt(3),sqrt(7)`

Answer» Correct Answer - A::B::C
Let a,b,c be pth,qth and rth terms of A.P. Then
a=A+(p-1)D,b=A+(q-1)D,c=A+(r-1)D
`rArr(r-q)/(q-p)=(c-b)/(b-a)` is rational number.
now for 1,6,19,`(r-q)/(q-p)=(19-6)/(6-1)` is a rational number.
For `sqrt2,sqrt(50),sqrt(98),(r-q)/(q-p)=(sqrt(98)-sqrt(50))/(sqrt(50)-sqrt2)=(7sqrt2-5sqrt2)/(5sqrt2-sqrt2)`
`=1/2` is a rational number.
For log2, log 16, log 128
`(r-q)/(q-p)=(log128-log16)/(log16-log2)=(7log2-4log2)/(4log2-log2)=1`
is a rational number.
But for `sqrt2,sqrt3,sqrt7,(r-q)/(q-p)` is not a rational number.


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