Question

Find the value of the middle term of the A.P. $7,13,19$,..., $247$.

Answer 1

we are given, the arithmetic series: $7,13,19.....247$

total terms $=n=$ $\frac{lastterm-firstterm}{d}+1$

$=\frac{247-7}{6}+1$

$=\frac{240}{6}+1$

$=40+1$

$=41$

now , for odd series middle term will be $\left(\frac{n+1}{2}\right)=\left(\frac{41+1}{2}\right)=\frac{42}{2}=21$

so here $a=7$, $d=6$, $a_n=a+(n-1)d$

21st term will be

$a_{21}=a+921-1)d$

$=\left(7\right)+\left(20\right)\left(6\right)$

$=127$

so the middle term of the series is $127$.