If $a$ and $b$ are two complex numbers, then the sum of $(n+1)$ terms of the series $a c_0-(a+d) c_1+(a+2 d) c_2-(a+3 d) c_3+$ $\_\_\_\_$ is

The value of

$$ 99^{50}-90 \cdot 98^{50}+\frac{99 \cdot 98}{1 \cdot 2}(97)^{50}-\ldots \ldots \ldots \ldots .+99 $$

is

If the coefficient of $x^2$ and $x^3$ in the expansion of $\left(1+8 x+b x^2\right)(1-3 x)^9$ in the power of $x$ are equal, then $b$ is

If the coefficients of $x^7$ and $x^8$ in the expansion of $\left[2+\frac{x}{3}\right]^n$ are equal, then value of $n$ is