1.

if five times the fifth term of an AP is equal to 8times its eighth term show that its 13th term is zero

Answer»

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)
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