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match the following . {:(,"columnI",...

match the following .
`{:(,"columnI",,"columnII"),((i) ,4.1.(1)/(4).(1)/(16),(a) ,AP),((ii) ,2.3.5.7,(b) ,"sequence "),((iii) ,13.8.3.-2.-7,( c) ,GP):}`

Text Solution

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(i) `4,1,(1)/(4),(1)/(16)`
`implies (T_(2))/(T_(1))=(1)/(4)implies (T_(3))/(T_(2))=(1)/(4)implies (T_(4))/(T_(3))=(1//16)/(1//4)=(1)/(4)`
Hence it is a GP .
(ii) 2,3,5,7
`therefore T_(2) -T_(1) =3-2=1`
` T_(3) -T_(1) =5-3=2`
`:' T_(2) -T_(1) ne T_(3) 0t_(2) `
hence it is not an AP.
Again , `(T_(2))/(T_(1))=3//2implies (T_(3))/(T_(2))=5//3`
`:' (T_(2))/(T_(1))ne (T_(3))/(T_(2))`
it is not a GP .
Hence it is a sequence
(iii) 13,8,3-2,-7
` T_(2)-T_(1)=8-13=-5`
`T_(3)-T_(2) =3-8=-5`
`:' T_(2) -T_(2)=T_(3)-T_(2) `
Hence ,it is an AP.
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