Question

I tried something similar to the notation of (x+2)^7, etc, did not get close at all, how would this be solved?

Answer 1

Answer:

C

Step-by-step explanation:

-24+96-384+...

a=-24

r=96/(-24)=-4

$s_{7}=a\frac{1-r^7}{1-r} \\=-24\frac{1-(-4)^7}{1-(-4)}\\=-24\frac{1+4^7}{1+4} \\=-24\frac{1+16384}{5} \\=-24\frac{16385}{5} \\=-24 \times 3277\\=-78648$

Answer 2

$24 = 3 \cdot 2^3$

$96=3\cdot 2^5$

$384=3\cdot2^7$

hence it is a geometric progression, with a multiplied constant $3$

Sum of G.P. of $n$ terms $S_n = a\dfrac{r^n-1}{r-1}\quad \text{where } r \text{ is the common ratio and } a \text{ is the first term}$

and $r=-2^2=-4$

Note that the constant should be separated, so

$a= -8 [\tex]after plugging the values, you'll get the answer [tex] -26216 \times 3$

which option C