Question

the ratio of 7th to 3rd term of an AP is 12:5 find the ratio of the 13th and 4th term

Answer 1

Refer to the image below for the answer.

Answer 2

Answer:

10:3

Step-by-step explanation:

Given : the ratio of 7th to 3rd term of an AP is 12:5

To Find:  find the ratio of the 13th and 4th term

Solution :

Formula of n th term in AP = a+(n-1)d

Where a is the first term

n is the term number

d is the common ratio

Now when n = 7

So,a+(7-1)d=a+6d

When n = 3

So,  a+(3-1)d=a+2d

Since we are given that the ratio of 7th to 3rd term of an AP is 12:5

⇒$\frac{a+6d}{a+2d} =\frac{12}{5}$

⇒5a+30d=12a+24d

⇒6d = 7a

⇒a=6d/7

Now 13th term =a+(13-1)d =a+12d =$\frac{6d}{7} +12d$

4th term =a+(4-1)d =a+3d =$\frac{6d}{7} +3d$

Now ratio of 13th and 4th term

$\frac{\frac{6d}{7} +12d}{\frac{6d}{7} +3d}$

$\frac{6d+84d}{6d+21d}$

$\frac{90d}{27d}$

$\frac{10}{3}$

Thus the ratio of the 13th and 4th term is 10:3