Question

What is the common difference of an ap in which a 21 - a 7 is equal to 84?

Answer 1

Answer:

So the Common difference is 6

Step-by-step explanation:

Given:

Terms are in ap which means arithmetic progression

Now given is

a₂₁ - a₇ = 84

To find:

Common difference = d=?

Solution:

If two terms are in ap then their is a common difference between them which is called d

Also if we have an arithmetic sequence which is an arithmetic progression too then its last term would be

aₙ = a₁ + (n-1)d

Now For our given we have

a₂₁ and a₇ the two terms

From the above formula

a₂₁ = a₁ +(21-1) d

a₂₁ = a₁ +20 d   .............(i)

Now similarly

a₇ = a₁ + (7-1) d

a₇ = a₁ + 6 d              ............(ii)

Now according to given Condition

a₂₁ - a₇ = 84

Putting in the values it gives us

(a₁ + 20 d) -(a₁ + 6 d)=84

a₁ + 20d - a₁ - 6d = 84

Cutting out the same terms and solving gives

20 d - 6 d =84

14 d = 84

Dividing both sides by 14

14d / 14 = 84 / 14

d = 6

So the Common difference is 6