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
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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
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Answer:
(a) d = 8
(b) 32
Given that,
▶ Difference between 5th term and 8th term of an AP is 24.
We have to find,
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.