Step-by-step explanation:

Given:-

The FOURTH and eighth terms of an A Pare in the ratio 1:2 and tenth TERM is 30.

To find:-

Find the Common difference ?

Solution:-

We KNOW that

a is the first term and d is the common difference of an AP then the general term = an = a+(n-1)d

Fourth term = a4 = a+3d

Eighth term = a8 = a+7d

The ratio of the fourth and eighth terms of an AP = 1:2

=> a4:a8 = 1:2

=> (a+3d):(a+7d) = 1:2

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

On applying cross multiplication then

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

=> 2a +6D = a+7d

=> 2a-a = 7d-6d

=> a = d----------(1)

Given that

Tenth term = 30

=> a10 = 30

=> a+9d = 30

On Substituting the value of a in the above formula

=> d+9d = 30

=> 10d = 30

=>d = 30/10

=> d = 3

Common difference = 3

Answer:-

The common difference for the given problem is 3

Check:-

We have a = d = 3

Now a4 = 3+3(3)=3+9=12

a8 = 3+7(3)=3+21=24

Their ratio = 12:24=1:2

a10 =3+9(3)=3+27=30

Verified the given relations

Used formula:-

• a is the first term and d is the common difference of an AP then the general term = an = a+(n-1)d