Question

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

Answer 1

Main concept used: To find the term from end, consider the given A.P. in reverse order and find the term. i.e., -100.... -6, -4, -2.
Now, a = -100
$d=a_{n+1}-a_n=-4-(-6)=-4+6=2$
$\therefore n=12$
$\Rightarrow a_n=a+(n-1)d$
$a_{1}2=-100+(12-1)\left(2\right)$
$=-100+11\times 2=-10022$
$\Rightarrow a_{12}=-78$
Hence, the 12th term from the last of A.P. -2, -4, -6, ...... -100 is -78.