in a certain A.P the 24th term is twice the 10th term. prove that the 72nd term is twice the 34th term.
please give me the answer with explanation
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let a be the first term and d the common difference
given
t24 = 2*t10
a+23d = 2*( a + 9d)
a + 23d = 2a + 18d
2a - a = 23d - 18d
a = 5d
now
t72/t34
= (a+71d)/(a+33d)
= (5d + 71d)/(5d + 33d). (since a= 5d)
= 76d / 38d
= 2
hence
t72 = 2* t34
proved
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