Question

4th and 8th term of AP are in the ratio of 1 is to 2 and 10th term is 30 find the common difference ​

Answer 1

As given

4th and 8th term of AP are in the ratio of 1 is to 2

a4 = a+3d

a8= a+7d

Ratio

(a+3d)/(a+7d) = 1/2

Cross multiply

2a +6d = a+7d

a= d

Also given that 10th term is 30

a10 = a+9d= 30

a=d

a+9a=30

So a = 3 and d= 3

Hence both first term and common difference is 3.

Thanks.

Answer 2

Answer:

$\frac{a+3d}{a+7d} =\frac{1}{2} \\2a+6d=a+7d\\a=d\\a+9d=30\\Since a=d,\\d+9d=30\\10d=30\\d=3$

The common difference is 3.

Step-by-step explanation:

Let the first term be a.

Let the common difference be d.