The 24th term of an A.P. is twice its 10th term. Show that its 72nd term is 4 times its 15th term.

Given: a24=2a10

a +23d= 2(a +9d)


5d=a (i)


To Prove:a72 =4a15


Proof: L.H.S. =a72


= a +71d


=5d +71d [from (i)]


=76d


R.H.S= 4a15


=4(a +14d)


=4a +56d


=4(5d) +56d [from (i)]


=20d +56d


=76d


Since, L.H.S=R.H.S.


Hence proved


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