Question

(iv) If five times the 5th term of an A.P. is equal to eight times its 8th term, then
show that its 13th term is zero.​

Answer 1

Answer:

The $13^{th}$ term is 0.

Step-by-step explanation:

The formula to compute the $n^{th}$ term of an AP is:

$T_{n}=a+(n-1)d$

Here, a = first term, d = common difference.

It is given that: $5T_{n} = 8T_{n}$

Solve this as follows:

$5T_{n} = 8T_{n}\\5[a+(5-1)d]=8[a+(8-1)d]\\5a+20d=8a+56d\\3a=-36d\\a=-12d$

Now compute the 13th term as follows:

$T_{13} = a + (13 - 1)d\\\ = -12d + 12d\\\ =0$

Hence proved that the 13th term is 0.

Answer 2

In the A.P ,if 5times the 5th term of an A.P is equal to the 8 Times of the 8th term of an A.P ,then 13th term in the A.P is shown in the attached file :-