Question

The difference between 5th term and 8th term of an AP is 24 (a) Find the common difference. (b)what is the difference between 8th term and 12 th term​

Answer 1

Answer:

(a) d = 8

(b) 32

Given that,

▶ Difference between 5th term and 8th term of an AP is 24.

We have to find,

• (a) Common difference
• (b) Difference between 8th term and 12th term.

First of all, We know

⇒ Nth term, aₙ = a + (n - 1)d

So, Using the above formula, The 5th and the 8th term would be a + 4d and a + 7d respectively.

⇒ 8th term - 5th term = 24

⇒ a + 7d - (a + 4d) = 24

⇒ a + 7d - a - 4d = 24

⇒ 7d - 4d = 24

⇒ 3d = 24

⇒ d = 8

Here, The question (a) is solved completely. Now let's move on to the next question (b), where we have to find the difference between the 8th term and the 12th term.

⇒ 12th term - 8th term

⇒ a + (12 - 1)d - (a + (8 - 1)d )

As, aₙ = a + (n - 1)d

⇒ a + 11d - a - 7d

⇒ 11d - 7d

⇒ 4d

⇒ 4(8) [ ∵ d = 8 ]

⇒ 32

Hence, The difference between 8th term and 12th term is 32.

Answer 2

Required Answer :-

Let the 5th and 8th term be a + 4d and a + 7d

Now

a + 4d - a + 7d = 24

a - a (7d - 4d) = 24

3d = 24

d = 24/3

d = 8

now,

a + (12 - 1)d - (a + (8 - 1)d )

a + 11d - a - 7d

11(8) - 7(8)

88 - 56

32

Difference = 32