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# Find the 12th Term from the End of the Following Arithmetic Progressions: 3, 5, 7, 9, ... 201 - CBSE Class 10 - Mathematics

ConceptSum of First n Terms of an AP

#### Question

Find the 12th term from the end of the following arithmetic progressions:

3, 5, 7, 9, ... 201

#### Solution

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

3, 5, 7, 9, ... 201

Here, to find the 12th 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 (an) = 201

Common difference  (d) = 5 - 3

=2

Now as we know

a_n = a + (n - 1)d

So for the last term

201 = 3 + (n - 1)2

201 = 3 + 2n - 2

201 = 1 + 2n

201 -1 = 2n

Furthur simplifying

200 = 2n

n = 200/2

n = 100

So, the 12th term from the end means the 89th term from the beginning.

So, for the 89th term (n = 89)

a_89 = 3 + (89 - 1)2

= 3 + (88)2

= 3 + 176

= 179

Therefore the 12th  term from the end of the given A.P is 179

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Solution Find the 12th Term from the End of the Following Arithmetic Progressions: 3, 5, 7, 9, ... 201 Concept: Sum of First n Terms of an AP.
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