Question

if five times the fifth term of an AP is equal to 8times its eighth term show that its 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)
Hope it helps
Mark me as brain list

Answer 2

First term be a

Common difference be d

By the Information

5[a + (5 -1 )d] = 8[a + (8 - 1)d]

5(a + 4d) = 8(a + 7d)

5a + 20d = 8a + 56d

3a = 36d

a = -12d

Hence 13th term :-

a + (13 - 1)d

= -12d + 12d

= 0

Solved