Identify a1 in a geometric series for which S8 = 42.5 and r = -0.5.

Question

anonymous · Answer

$s_8=s_1\times r^7$

rainbow_dash · Answer

ohhh raised to the 7. i didn't know what to do because of the lack of an n :3

anonymous · Answer

so 
$$s_1=\frac{s_8}{r^7}$$ in your case $s_1=\frac{42.5}{(-.5)^7}$

anonymous · Answer

$s_1,s_2,s_3,s_4,...$
$s_1,s_1r,s_2r^2,s_3r^3,...$

rainbow_dash · Answer

that can't be right...i got -6071 for the -.5^7, but the highest possible answer is 63.75

anonymous · Answer

you put it in the calculator wrong
$(-.5)^7$ is a little tiny number

rainbow_dash · Answer

i meant 42.5/that tiny number :( my mistake

anonymous · Answer

maybe i read the problem wrong
maybe it is $\sum_{k=1}^8a_k=42.5$

rainbow_dash · Answer

oh god that sigma is scary.

anonymous · Answer

it is the 8th partial sum maybe

rainbow_dash · Answer

sorry but what does this mean?

anonymous · Answer

$$a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8=42.5$$

anonymous · Answer

formula is 
$$\frac{1-a^{n+1}}{1-r}$$ so you get 
$$\frac{1-a_1(-.5)^8}{1+.5}=42.5$$

anonymous · Answer

solve this for $a_1$

anonymous · Answer

oh damn that is wrong, first term is not 1, sorry 
$$\frac{a_1(1-a_1(-.5)^8)}{1-(-.5)}=42.5$$

anonymous · Answer

$$S_n = \frac{a(1-r^n)}{1-r}$$

anonymous · Answer

That a is $a_1$