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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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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 (Latest))
Chapter 5: Arithmetic Progressions
Ex. 5.2 | Q: 5.2 | Page no. 106
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Solution Find the number of terms in each of the following A.P. 18,15 1/2, 13, . . . , – 47 Concept: nth Term of an AP.
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