Question

If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term. *​

Answer 1

Answer: 0

Step-by-step explanation:  

Given : 7 × a₇ = 5 × a₅

Solution:

7 x (a+(7-1)d) = 5 x (a+(5-1)d)

7a + 42d= 5a + 20d

2a= -22d

a=-11d--------> 1

a₁₂=a+(12-1)d=a+11d=-11d +11d[From 1]=0

Answer 2

0 is the 12th term.

According to the data which is given in the question :

The 7 times of the 7th term of the AP is equal to 5 times of the 5th term.

Numerically it will be written as :

Let's take 1st term of the AP as "a".

And the common difference is "d".

so, the 7th term will be = a+(7-1)d, here n=7

and the 5th term =a+4d

7(a+6d)=5(a+4d)

7a+42d=5a+20d

2a=-22d

a=-11d

We are asked to find the 12th term

That will be written as a+11d

so, 12th term =-11d+11d=0 (ANSWER)