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# Find the number of terms in each of the following A.P. 18,15 1/2, 13, . . . , – 47 - Mathematics

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#### Question

Find the number of terms in each of the following A.P. 18,15 1/2, 13, . . . , – 47

#### Solution

For this A.P.

a = 18

d = a_2-a_1=15 1/2-18

d = (31-36)/2 = -5/2

Let there are n terms in this A.P.

Therefore, an = −47 and we know that,

an = a + (n − 1) d

-47 = 18 + (n - 1) (-5/2)

-47 - 18 = (n - 1) (-5/2)

-65 = (n - 1)(-5/2)

(n - 1) = (-130)/-5

(n - 1) = 26

n = 27

Therefore, this given A.P. has 27 terms in it.

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