Question

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

Answer 1

Answer:

5th term of an AP=a+4d

8th term of AP=a+7d

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

5a+20d=8a+56d

5a-8a=56d-20d

-3a=36d

a=-12d

13th term of an AP=a+12d=-12d+12d=0

hence proved

Answer 2

Answer:

Step-by-step explanation:

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