Question

A sequence starts from $\frac{1}{2}$ and $\frac{3}{4}$ is added to every term. Find the sequence.

• A. None
• B. $\frac{1}{2},\frac{5}{4},\frac{6}{4}\cdots \cdots$
• C. $\frac{1}{2},1,\frac{5}{4}\cdots \cdots$
• D. $\frac{1}{2},\frac{5}{4},2,\frac{11}{4},\frac{14}{4}\cdots \cdots$

Answer 1

The correct option is D

$\frac{1}{2},\frac{5}{4},2,\frac{11}{4},\frac{14}{4}\cdots \cdots$

Given,

1st term = $\frac{1}{2}$

term to be added = $\frac{3}{4}$

$\frac{1}{2}+\frac{3}{4}=\frac{5}{4}$

$\frac{5}{4}+\frac{3}{4}=\frac{8}{4}=2$

$\frac{8}{4}+\frac{3}{4}=\frac{11}{4}$

$\frac{11}{4}+\frac{3}{4}=\frac{14}{4}$

So the sequence is $\frac{1}{2},\frac{5}{4},2,\frac{11}{4},\frac{14}{4}\cdots \cdots$