If the three consecutive coefficients in the expansion of (1 + x)ⁿ are 28, 56, and 70, then the value of n is _______.

Let the three consecutive coefficients be${ }^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}-1}=28$,

${ }^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}}=56{\text{ and }}^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}+1}=70$

so that $\frac{{ }^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}}}{{ }^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}-1}}=\frac{\mathrm{n}-\mathrm{r}+1}{\mathrm{r}}=\frac{56}{28}=2$ and

$\frac{{ }^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}+1}}{{ }^{\mathrm{n}}{\mathrm{C}}_{\mathrm{r}}}=\frac{\mathrm{n}-\mathrm{r}}{\mathrm{r}+1}=\frac{70}{56}=\frac{5}{4}$

This gives n + 1 = 3r and 4n - 5 = 9r. Therefore,

$\frac{4\mathrm{n}-5}{\mathrm{n}+1}=3\text{ or }\mathrm{n}=8$