Sum of unknowns

Algebra Level 2

If the first two terms of the expansion of $(2+ax)^n$ are $64+576x$ , find the value of $n+a$ .

1 solution

Noel Lo
Apr 23, 2015

$2^n = 64$

$2^n = 2^6$

$n=6$

$6C1 \times 2^{6-1} k= 576$

$6 \times 2^5 k=576$

$192k = 576$

$k=\frac{576}{192} = 3$

$n+k = 6+3 = \boxed{9}$