Answer in Brief

Find where 0 (zero) is a term of the A.P. 40, 37, 34, 31, ..... .

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#### Solution

Let *a* be the first term and *d* be the common difference.

We know that, *n*^{th }term = *a*_{n }= *a* + (*n* − 1)*d*

It is given that *a* = 40, *d* = −3 and *a _{n}* = 0

According to the question,

⇒ 0 = 40 + (

*n*− 1)(−3)

⇒ 0 = 40 − 3

*n*+ 3

⇒ 3

*n*= 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, ..... .

Concept: Sum of First n Terms of an AP

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