Question

Find $n$ if the given value of $x$ is the $n$th term of the given A.P.
$5\frac{1}{2},11,16,16\frac{1}{2},22,.....;x=550$

Answer 1

Ans.

given A.P

$5\frac{1}{2},11,16\frac{1}{2},22,...\dots \dots .;x=550$

first term of this A.P is $a_1=5\frac{1}{2}=\frac{10+1}{2}=\frac{11}{2}$

second term of this A.P is $a_2=11$

nth term of this A.P is $a_n=x=550$

common difference of A.P

$d=a_2-a_1=\left(11\right)-\left(\frac{11}{2}\right)=\frac{22-11}{2}$

$⟹d=\frac{11}{2}$

the nth term of an A.P is given by

$a_n=a_1+(n-1)d$

put $a_n=550;a_1=\frac{11}{2};d=\frac{11}{2}$ in above equation we get

$⟹550=\frac{11}{2}+(n-1)\left(\frac{11}{2}\right)$

$⟹550=\frac{11}{2}+\frac{11}{2}n-\frac{11}{2}$

$⟹550=\frac{11}{2}n$

$⟹11n=550\times 2$

$⟹n=\frac{1100}{11}$

$⟹n=100$