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Question
Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .
Solution
Let a be the first term and d be the common difference.
We know that, nth term = an = a + (n − 1)d
It is given that a = 40, d = −3 and an = 0
According to the question,
⇒ 0 = 40 + (n − 1)(−3)
⇒ 0 = 40 − 3n + 3
⇒ 3n = 43
⇒ n = \[\frac{43}{3}\] .... (1)
Here, n is the number of terms, so must be an integer.
Thus, there is no term where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .
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