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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.
Solution:
a = 18
d = a2-a1
d = (31-36)/2 = -5/2
Let n terms be in this A.P.
an = 205
For an A.P we know:-
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
The A.P. has 27 terms in its given series.