Does there exist a geometric progression containing 27,8 and 12 as three of its terms?
Open in App
Solution
Let if possible 8 be the first term and 12 and 27 be mth and nth terms respectively. ∴12=arm−1=8rm−1,27=8rn−1⇒32=rm−1,(32)3=rn−1=r3(m−1) ⇒n−1=3m−3 or 3m=n+2orm1=n+23=k say ⇒m=k,n=3k−2 By giving k different values we get integral values of m and n.
Hence there can be infinite number of G.P's whose any three terms will be 8,12,27 (not consecutive).