Question

Find the middle term of the AP 10, 7, 4, ... , (-62).

Answer 1

Let "a" be the first term that is 10, d be the common difference that is 7-10=-3, $a_n$ be last term that is -62 and n be the number of terms.

We're having $a_n=a+(n-1)d$

-62=10+(n-1)(-3)

-62-10=(n-1)(-3)

$\frac{-72}{-3}=(n-1)$

24+1=n

n=25

Now the number of terms are 25, it is odd and if we have to find the middle term then we has to do this

$Middleterm=\frac{numberofterms+1}{2}$

Middle term $=\frac{25+1}{2}=\frac{26}{2}=13$

now lets find the value of 13th term

$a_{13}=10+(13-1)(-3)$

$a_{13}=10+\left(12\right)(-3)$

$a_{13}=10-36$

$a_{13}=-26$

The middle term that is 13th term that is -26.