Question

Find the ${12}^{th}$ term from the end of the A.P $-2,-4,-6,...-100.$

Answer 1

Given A.P is $-2,-4,-6,....100$.

To find the term from end, consider the given A.P. in reverse order and find the term. i.e., $-100,-\mathrm{98....}-6,-4,-2.$

First term, $a=-100$

Common difference, $d=a_2-a_1$

$=-98-(-100)=-98+100=2$

$n^{th}$ term of an AP is given by $a_n=a+(n-1)d$

Here, $a=-100,d=2,n=12$

Now, $a_{12}=-100+(12-1)\left(2\right)$

$=-100+11\left(2\right)$

$=-100+22$

$=-78$

Therefore, ${12}^{th}$ term from end of the given AP is $-78$.