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# Find the 12th Term from the End of the Following Arithmetic Progressions: 1, 4, 7, 10, ..., 88 - CBSE Class 10 - Mathematics

#### Question

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

1, 4, 7, 10, ..., 88

#### Solution

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

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) = 1

Last term (a_n) = 88

Common difference , d = 4 -1 = 3

Now as we know

a_n = a + (n -1)d

So for the last term

88 = 1 + (n - 1)3

88 = 1 + 3n - 3

88 = -2 + 3n

88 + 2 = 3n

Furthur simplifying

90 = 3n

n = 90/3

n = 30

So the 12 th term from tje end means the 19th term from the beginning.

so for the 19th term (n = 19)

a_19 = 1 + (19 - 1)3

= 1 + (18)3

= 1 + 54

= 55

Therefore the 12th term from the end of the giving A.P is 55

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Solution Find the 12th Term from the End of the Following Arithmetic Progressions: 1, 4, 7, 10, ..., 88 Concept: nth Term of an AP.
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