The 4th and 8th term of an ap is in ratio 1:2.the tenth term is 30.find the common difference?

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Answer 1 · 2018-03-23T12:52:20

#3#.

4th and 8th term of an AP is in ratio 1:2.

That is, #a_4 : a_8 = 1:2#

So,

#=>(a+3d)/(a+7d) = 1/2#

#=>2(a+3d)=(a+7d)#

#=>2a+6d=a+7d#

#=>a=d#

The tenth term is 30

That is, #a_10 = 30#

#=> a+9d = 30#

#=> a+9a = 30# [since #a=d#]

#=> 10a = 30 #

#=> a=3#

Therefore,

since #a=d#,

#"common difference" = 3#