The 4th term of an A.P. is 22 and the 15th term is 66. Find the first terns and the common

difference. Hence find the sum of the series to 8 terms.

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#### Solution

Let a be the first term and d be the common difference of given A.P.

Now,

4th term = 22

⇒ a + 3d = 22 ...(i)

15th term = 66

⇒ a + 14d = 66

Subtracting (i) from (ii), we have

11d = 44

⇒ d = 4

Substituting the value of d in (1) we get

a = 22 - 3 x 4 = 22 - 12 =10

⇒ First term = 10

Now

Sum of 8 terms = `8/2[2xx10+7xx4]` = 4[20+28] = 4x48=192

Concept: Nature of Roots

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