Question

If the three consecutive coefficient in the expansion of $(1+x{)}^n$ are 28, 56 and 70, then the value of n is

• A. 6
• B. 4
• C. 8
• D. 10

Answer 1

The correct option is C

8

Let the three consecutive coefficients be

${}^n{C}_{r-1}$ = 28, ${}^n{C}_r$ = 56 and ${}^n{C}_{r+1}$ = 70, so that

$\frac{{}^n{C}_r}{{}^n{C}_{r-1}}$ = $\frac{n-r+1}{r}$ = $\frac{56}{28}$ = 2

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

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

∴ $\frac{4n-5}{n+1}$ = 3 ⇒ n = 8