What is the 41st term of the arithmetic sequence where a1 = 16 and a15 = -40

Question

hartnn · Answer

you know the n'th term formula ?

hartnn · Answer

$\Large a_n = a_1 + (n-1)d$

plug in n = 15, 
a1 = 1st term = 15
a15 = -40 = left side

anonymous · Answer

so it would be -40=16+(15-1)d

hartnn · Answer

correct! find 'd'

anonymous · Answer

-4

hartnn · Answer

yes,
now use the same formula again

hartnn · Answer

this time you need 41st term
so plug in n=41

hartnn · Answer

d=-4
a1 =16

anonymous · Answer

-144?

hartnn · Answer

$\huge \checkmark $

anonymous · Answer

What is the sum of an 8-term geometric series if the first term is 14 and the last term is -3,919,104

hartnn · Answer

you will need to find 'r' = common ratio first

use the formula 
$a_n = a_1 r^{n-1}$
n= 8 
a1 = 1st term = 14 an = last term = a8 = -3,919,104

anonymous · Answer

i got like 3700 something weird number

hartnn · Answer

for 'r' ?

anonymous · Answer

yeah lemme try again

hartnn · Answer

sure, i am getting an integer
a negative integer

anonymous · Answer

yeah like -3703 ei

hartnn · Answer

lol, i am getting r = -6

hartnn · Answer

$-3,919,104 = 14 r^7  \ \Large r =\sqrt[7]{\dfrac{-3,919,104}{14}} = -6 $

anonymous · Answer

oohhhh

anonymous · Answer

so now don't i plug in -6 into the formula

hartnn · Answer

now use the sum formula 
$\Large S_n = a_1 \dfrac{r^n-1}{r-1}$
r= -6
a1 =14
n=8

anonymous · Answer

14   -1679616-1/-7

hartnn · Answer

ok, and what does that equal?

anonymous · Answer

i keep getting 3,359,234

hartnn · Answer

$\huge \checkmark $

hartnn · Answer

thats correct, why do u doubt ?

anonymous · Answer

cause thats not one of my answers given

hartnn · Answer

ohh? 
let me check all the work again

hartnn · Answer

r =- 6 is surely correct

hartnn · Answer

for sum i got 
$\Large -3359230$

anonymous · Answer

okay thats one of them!

hartnn · Answer

http://www.wolframalpha.com/input/?i=%5B%28-6%29%5E8+-1%5D*%2814%29%2F%28-7%29

anonymous · Answer

A lottery winner must decide between two methods of payment. Choice one is to receive a lump sum of $100,000,000. Choice two is to begin with one cent on day 1, four cents on day 2, 16 cents on day three, and so on until the end of 16 days. Which choice should the lottery winner select? Using complete sentences, explain the procedure taken to answer this question.

hartnn · Answer

can you ask this as a new question ? so that others can help you too ? sorry i need to go now...