the 4th term of an A.P. is zero .Prove that the 25th term of the A.P. is tree times its 11th term
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a=first term
d=COMMON difference
So 4th term=a+3d
0=a+3d
a= -3d
now
25th term =a+24d
=-3d+24d
=21d
now 11th term = a +10d
=10d-3d
=7d
so 11th term =7
11th term =21/3
3(11th term)=21
but 21=25th term
so 3(11th term)=25th term
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