Question

Find the common difference and $99th$ term of the arithmetic progression :
$7\frac{3}{4},9\frac{1}{2},11\frac{1}{4},\dots \dots \dots \dots \dots \dots$.

Answer 1

$7\frac{3}{4},9\frac{1}{2},11\frac{1}{4},\dots \dots \dots \dots \dots \dots$.Given,A.P

i.e.,$31/4,19/2,45/4,$ …….

So,

$a=31/4$

Common difference, $d=19/2–31/4=(38–31)/4=7/4$

Then the general term of the A.P

$t_n=a+(n–1)d$

$t_n=31/4+(n–1)\left(7/4\right)=31/4+7n/4–7/4=7n/4+31/4–7/4=7n/4+(31–7)/4=7n/4+\left(24\right)/4$

$t_n=7n/4+6$

Hence, the $99th$ term is $7\left(99\right)/4+6=693/4+6=717/4$