Question

If 6times of sixth term of an AP is equal to 8 times of its eighth term ,then show that the 14th term of it is zero

Answer 1

Answer:

The 14th term of the AP is 0.

Step-by-step explanation:

The nth term of an AP is:

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

Given:

6T₆ = 8T₈

Then,

$6T_{6}=8T_{8}\\6(a+(6-1)d)=8(a+(8-1)d)\\6a+30d=8a+56d\\2a=-26d\\a=-13d$

Compute the 14th term as follows:

$T_{14}=a+(14-1)d\\=a+13d\\=-13d+13d\\=0$

Thus, the 14th term of the AP is 0.

Answer 2

Answer:

=> 6 (a+5d) = 8(a+7d)

=> 6a+ 30d = 8a+56d

=> 6a-8a = 30d-56d

=> 2a = 13d

=> a = 13d

but 14th term. = a+13d

:: value of 14th term = 0