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Mathematics 16 Online
OpenStudy (anonymous):

Please Someone HELP! im exhausted its 12 my time!! Please help! Have some sympathy!

OpenStudy (anonymous):

14. What is S5 for 1000 + 500 + 250 + ... ?

hartnn (hartnn):

did you realize that this is geometric sequence with common ratio =... ?

OpenStudy (anonymous):

no i didn't

OpenStudy (anonymous):

so r=.5

hartnn (hartnn):

yes, now do you know the general formula of n'th term of geometric series ?

OpenStudy (anonymous):

1000+500+250+125+62.5

OpenStudy (anonymous):

no i dont

hartnn (hartnn):

the formula for sum is \(S_n = a_1\dfrac{r^{n}-1}{r-1}\) since you need 5 terms sum, n = 5 you already know r = 0.5 and a1 = 1st term = 1000 just plug in values!

OpenStudy (anonymous):

i got -3000 thats not an option though

hartnn (hartnn):

lets check, 1000 (-0.5^5+1)/0.5 = 2000 * 0.96875 = 1937.5 ? is that an option?

OpenStudy (anonymous):

yeah it is!! can u help with 2 more please!

OpenStudy (anonymous):

hartnn (hartnn):

yeah, but u need to try them first on your own....you can surely ask for formulas...

OpenStudy (anonymous):

the attachment is the question

hartnn (hartnn):

the series is 2,1,1/2,1/4.... total 16 terms, n=16 a1 = 1st term = 2, r=... ? then use the same formula.

OpenStudy (anonymous):

there is none right?

OpenStudy (anonymous):

there is no common ratio

hartnn (hartnn):

isn't it 1/2 or 0.5 ?

OpenStudy (anonymous):

oh oh oops!

OpenStudy (anonymous):

I got -0.00012207

OpenStudy (anonymous):

and it rounds to 0

OpenStudy (anonymous):

is that correct

OpenStudy (anonymous):

@hartnn

hartnn (hartnn):

wait, let me calculate.

hartnn (hartnn):

i am getting approximately 4...

hartnn (hartnn):

how u got 0 ?

OpenStudy (anonymous):

i dont know! Im so tired I can barley think..... I need to turn this in tommorrow morning!

hartnn (hartnn):

try, sum as 4.

OpenStudy (anonymous):

ok... 11. What is the sum of the finite arithmetic series? (–5) + 0 + 5 + 10 + ... + 65

OpenStudy (anonymous):

here are the choices 900 455 450 445

hartnn (hartnn):

whats the common difference ?

OpenStudy (anonymous):

D=5

hartnn (hartnn):

yes, formula is S = (n/2) [1st term + last term] S =... ?

OpenStudy (anonymous):

1,950

OpenStudy (anonymous):

s=65/2{-5+65}

hartnn (hartnn):

n= 15 15/2 * (60) = 15*30 =.... ?

OpenStudy (anonymous):

450

OpenStudy (anonymous):

OpenStudy (anonymous):

im not typing... have no idea why its doing that

OpenStudy (anonymous):

last one I promise

OpenStudy (anonymous):

please @hartnn promise its the last

hartnn (hartnn):

just a sec, i am solving....

hartnn (hartnn):

the series is -1,2,5,8.... so common difference d=.... ?

OpenStudy (anonymous):

d=3

hartnn (hartnn):

yes, a1 = 1st term = -1, n =18 formula is : \(\S_n = (n/2)[2a+(n-1)d]\) just plug in values!

OpenStudy (anonymous):

441!

hartnn (hartnn):

yes :)

OpenStudy (anonymous):

thanks sooo much now I may sleep! :) thank you thank you thank you!

hartnn (hartnn):

your welcome ^_^ have sweet dreams :)

OpenStudy (anonymous):

thanx :)

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