# Arithmetic Progressions

#### Answer:

In the given problem, we need to find the 12^{th} term from the end for the given A.P.

(i) 3, 5, 7, 9 …201

Here, to find the 12^{th} term from the end let us first find the total number of terms. Let us take the total number of terms as *n*.

So,

First term (*a*) = 3

Last term (*a*_{n}) = 201

Common difference (*d*) =

Now, as we know,

So, for the last term,

Further simplifying,

So, the 12^{th} term from the end means the 89^{th} term from the beg...

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