This question is from NCERT Book class 10th Ch. number 5 Ex. 5.2 Q. 5 (ii). In the following question you have to find the number of terms in the given series and give its solution briefly.

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Solution:a = 18

d = a

_{2}-a_{1 }d = (31-36)/2 = -5/2

Let n terms be in this A.P.

a

_{n}= 205For an A.P we know:-

a

_{n}= 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

The A.P. has 27 terms in its given series.