Question

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

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

Answer 1

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

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) = 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

Further simplifying,

90 = 3n

`n = 90/3`

n = 30

So, the 12^th term from the end means the 19^th term from the beginning.

So, for the 19^th term (n = 19)

`a_19 = 1 + (19 - 1)3`

`= 1 + (18)3`

= 1 + 54

= 55

Therefore, the 12^th term from the end of the given A.P. is 55.