Question

Find the middle terms of the A.P. $7,13,19,....,241$.

• A. $411,127$
• B. $121,227$
• C. $121,127$
• D. $321,127$

Answer 1

Answer: (C)

$121,127$

Given A.P :- $7,13,19,........241$

$\therefore a=7$ $t_n=241$ $d=13-7=6$

$\therefore t_n=a+(n-1)d$

$\therefore 241=7+(n-1)6$

$\therefore \frac{241-7}{6}=n-1$

$\therefore \frac{234}{6}=n-1$

$\therefore 39+1=n;n=40$

$\therefore \frac{n}{2}=\frac{40}{2}=20$......(middle term)

$\therefore \frac{n}{2}+1=21$ .....(middle term)

$\therefore t_{20}=7+(20-1)6$

$\therefore t_{20}=7+19\times 6$

$\therefore t_{20}=7+114=121$

$\therefore t_{21}=121+6=127$

$\therefore$ Middle terms are $121$ and $127$.