Question
Find six rational numbers between 2 and 3.
✓
Answer
x = 2, y = 3 and n = 6$\text{d}=\frac{\text{y}-\text{x}}{\text{n}+1}=\frac{3-2}{6+1}=\frac{1}{7}$
Thus, the required numbers are$(\text{x}+\text{d}),(\text{x}+2\text{d}),(\text{x}+3\text{d}),...,(\text{x}+\text{n}\text{d})$
$=\Big(2+\frac{1}{7}\Big),\Big(2+2\times\frac{1}{7}\Big),\Big(2+3\times\frac{1}{7}\Big),\\\Big(2+4\times\frac{1}{7}\Big),\Big(2+5\times\frac{1}{7}\Big),\Big(2+6\times\frac{1}{7}\Big)$
$=\frac{15}{7},\frac{16}{7},\frac{17}{7},\frac{18}{7},\frac{19}{7},\frac{20}{7}$
Thus, the required numbers are$(\text{x}+\text{d}),(\text{x}+2\text{d}),(\text{x}+3\text{d}),...,(\text{x}+\text{n}\text{d})$
$=\Big(2+\frac{1}{7}\Big),\Big(2+2\times\frac{1}{7}\Big),\Big(2+3\times\frac{1}{7}\Big),\\\Big(2+4\times\frac{1}{7}\Big),\Big(2+5\times\frac{1}{7}\Big),\Big(2+6\times\frac{1}{7}\Big)$
$=\frac{15}{7},\frac{16}{7},\frac{17}{7},\frac{18}{7},\frac{19}{7},\frac{20}{7}$
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