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

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#### 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, *a*_{n} = −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.

Concept: nth Term of an AP

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