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Question
Find n if the given value of x is the nth term of the given A.P.
−1, −3, −5, −7, ...; x = −151
Solution
In the given problem, we need to find the number of terms in an A.P
-1, -3, -5, -7 …
We are given,
`a_n = -151`
Let us take the total number of terms as n.
So,
First term (a) = −1
Last term (an) = −151
Common difference (d) = -3 - (-1)
= -3 + 1
= -2
Now as we know
`a_n = a + (n - 1)d``
SO for the last term
`-151 = -1 + (n - 1)(-2)`
-151 = -1 - 2n + 2
-151 = - 2n
-2n = 151 - 1
On further simplifying, we get,
-2n = -152
`n = (-152)/(-2)`
n = 76
Therefore, the total number of terms of the given A.P. is n = 76
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