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