Question

State whether the statement is True/False.

The 10th term of the HP $\frac{3}{2},1,\frac{3}{4},\frac{3}{5},...$ is $\frac{3}{11}$.

• A. True
• B. False

Answer 1

The correct option is A True

The given HP is $\frac{3}{2},1,\frac{3}{4},\frac{3}{5},...$

The corresponding AP is $\frac{2}{3},1,\frac{4}{3},\frac{5}{3},...$

Here, $a=\frac{2}{3},d=1-\frac{2}{3}=\frac{1}{3}$

Therefore,

$T_{10}$ of the corresponding AP is

$a+(10-1)d=\frac{2}{3}+\left(9\right)\frac{1}{3}=\frac{11}{3}$.

Hence, 10th term in HP is $\frac{3}{11}$.