Find the 12th term from the end of the following arithmetic progressions:
3, 8, 13, ..., 253
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Solution
In the given problem, we need to find the 12th term from the end for the given A.P.
3, 8, 13 …253
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 (`a_n`) = 253
Common difference d = 8 - 3
= 5
Now as we know
`a_n = a + (n - 1)d`
So for the last term
253 = 3 + (n - 1)5
253 = 3 + 5n - 5
253 + 2 = 5n
Further simplifying
255 = 5n
`n = 255/5`
n = 51
So, the 12th term from the end means the 40th term from the beginning.
So, for the 40th term (n = 40)
`a_40 = 3 + (40 - 1)5`
`= 3 + (39)5`
= 3 + 195
= 198
Therefore the 12th term from the end ofthe given A.P.is 198.
Concept: nth Term of an AP
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