Find the 5th term from the last term of the finite AP $ 85,80,75, \ldots,-30 $.

Given:

Given AP is \( 85,80,75, \ldots,-30 \).

To do:

We have to find the 5th term from the last term of the finite AP.

Solution:

Writing the AP in the reverse order, we get,

\( -30,\ldots,75,80,85 \).

Let the common difference of this AP be $d$.

This implies,

$d=80-85=-5$

5th term from the last term of the finite AP \( 85,80,75, \ldots,-30 \) is the 5th term of the reverse AP.

We know that,

nth term of an A.P. $a_n=a+(n-1)d$

Therefore,

$a_{5}=a+(5-1)d$

$=a+4d$

$=85+4(-5)$

$=85-20$

$=65$

The 5th term from the last term of the finite AP \( 85,80,75, \ldots,-30 \) is 65.

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Updated on: 10-Oct-2022

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