Question

Find the sum

-16+4-(4/4)+(4/4^2)-(4/4^3)+....-(4/4^19)

Answer 1

It looks like the common ratio is -1/4... each term is multiplied by -1/4 to get the next one. So you can just use a geometric series sum (idk if you have to show calculusey proof of it...)

Answer 2

yeah ive gt the common ratio but idk how to find the sum....and nah its online homework

Answer 3

@agent0smith smarticles!

Answer 4

Use the sum formula for a geometric series \[\Large S_n = \frac{ a_n (1- r^n) }{ 1-r }\] from memory that's it... i'll check.

Answer 5

that looks familiar! lol

Answer 6

I was a bit off.... http://www.regentsprep.org/regents/math/algtrig/ATP2/ArithG12.gif \[\Large S_n = \frac{ a_1 (1- r^n) }{ 1-r }\]

Answer 7

okay:) now what lol

Answer 8

is a1 the first term?

Answer 9

a1 is the first term.. which is?

r we know is -1/4

n is the number of terms, which we can find

Answer 10

is it -16?

Answer 11

a1 = -16 yep. r=-1/4

and the last term is -(4/4^19) which we can use to find n

Answer 12

math teacher skills smh

Answer 13

okay:)

Answer 14

K so we just need to find n, the number of terms...

Answer 15

21 terms?

Answer 16

I think so... 21 looks right. Now plug it all into the formula

Answer 17

(-16(1-(-1/4)^21))/(1-(-1/4))

Answer 18

=-12.80000 yay its right! thank you so much!

Answer 19

:)

Answer 20

can you help me with one more? ill post it on a different thing!