The numbers 1, 4, 16 can be three terms (not necessarily consecutive) of no A.P. only on G.P. infinite number o A.P.s infinite number of G.P.s

Options

A. no. A.P
B. only one G.P
C. infinite number of A.P's
D. infinite nuber of G.P' s

Answer

C, D

Explanation

`4=1+(n-1)d,16=1+(m-1)d`
`rArr15/3=(m-1)/(n-1)` or
`(n-1)/1=(m-1)/5`=p= positive integer.
`thereforen=p+1,m=5p+1`. So, n,m have infinite pairs of values.
also, 4=1`cdotr^(n),16=1cdotr^(m)`
`rArrr^(2n)=r^(m)rArr2n=m`
`thereforem/2=n/1=q`= Positive integer.
So,m,m have infinite pairs of values.