Question

if five times the 5th term of an A. P is equal to eight times its 8th term then show that it's 13th term is zero

Answer 1

Let of the AP
first term= a
common difference=d
ATQ
5[a+(5-1)d]=8[a+(8-1)d]
5(a+4d)=8(a+7d)
5a + 20d = 8a + 56d
3a = 36d
a= -12d
Now 13th term
a+(13-1)d
=-12d+12d
=0
(proved)