In exercise 5.2 of arithmetic progressions of class 10th. How i solve this important question of class 10th, because it is very important as regarding to board exams Find the number of terms in each of the following A.P.
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First term, a = 18
Common difference, d = a2-a1 =
d = (31-36)/2 = -5/2
Let there are n terms in this A.P.
an = 205
As we know, for an A.P.,
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.