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

C

Explanation:

-24+96-384+...

a=-24

r=96/(-24)=-4

`s_(7)=a(1-r^7)/(1-r) \\=-24(1-(-4)^7)/(1-(-4))\\=-24(1+4^7)/(1+4) \\=-24(1+16384)/(5) \\=-24(16385)/(5) \\=-24 * 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(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]</p><p></p><p></p><p>after plugging the values, you'll get the answer</p><p></p><p> [tex] -26216 * 3`

which option C