Question

For an A.P., the seventh term is 19 and the thirteenth term is 37. Find its twenty second term.

• A. 60
• B. 54
• C. 64
• D. 78

Answer 1

The correct option is C 64

For the given A.P., $T_7=19$ and $T_{13}=37$
Now $T_n=a+(n-1)d$
$\therefore T_7=a+(7-1)d$
$\therefore 19=a+6d$
$\therefore a+6d=19$ ............ (1)
Again, $T_{13}=a+(13-1)d$
$\therefore 37=a+12d$
$\therefore a+12d=37$ ............. (2)
Subtracting eq. (1) from eq. (2)
$a+12d=37$
$a+6d=19$

$6d=18$

$\therefore d=13$
Substituting $d=13$ in $a+6d=19$,
$a+6\left(3\right)=19$
$\therefore a+18=19$
$\therefore a=1$
Thus, the first term of the A.P. is 1 and the common difference is 3.
Now, $T_{22}=a+(22-1)d=1+(22-1)\left(3\right)$
$=1+\left(21\right)\left(3\right)=1+63=64$
Thus, the twenty second term of the given A.P. is 64.