anonymous
  • anonymous
What is the sum of a 6-term geometric sequence if the first term is 11, the last term is –11,264 and the common ratio is –4?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
sum=a(1-r)^n/(1-r) where a is the first term r is the common ratio and n is the number of terms
anonymous
  • anonymous
did i do something wrong ? Sn= a(1 - r^n) ------------- 1- r Sn= 11(1 - (-4)^6) ------------- 1- (-4) Sn= 11(1 - (-4096)) ------------- 5 Sn= 11(4097) ------------- 5 Sn= 11(4097) ------------- 5
ganeshie8
  • ganeshie8
hint : (-4)^6 = 4^6 = 4096

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ganeshie8
  • ganeshie8
Sn= a(1 - r^n) ------------- 1- r Sn= 11(1 - (-4)^6) ------------- 1- (-4) Sn= 11(1 - (4096)) ------------- 5 Sn= 11(-4095) ------------- 5
anonymous
  • anonymous
99099 ?
ganeshie8
  • ganeshie8
im getting -9009
anonymous
  • anonymous
ohh noo . i see my mistake . your righht . What is the sum of an 8-term geometric sequence if the first term is 10 and the last term is 781,250? how do i answer this with out the common ration ?
ganeshie8
  • ganeshie8
we need to find r first
ganeshie8
  • ganeshie8
\(a_8 = 10 \times r^7 = 781250\) => \( r^7 = 78125\) \(r = 5\)
ganeshie8
  • ganeshie8
Now try to find the sum using the usual sum formula
anonymous
  • anonymous
one sec .
ganeshie8
  • ganeshie8
yo
anonymous
  • anonymous
im sorry . are you here @ganeshie8 ?
ganeshie8
  • ganeshie8
yea
ganeshie8
  • ganeshie8
its okay :)
anonymous
  • anonymous
Sn= a(1 - r^n) ------------- 1- 5 Sn= 10(1 - 5^8) ------------- -4 Sn= 10(1 - 390625) ------------- -4 Sn= 10(- 390624) ------------- -4 am i right so far right ?
ganeshie8
  • ganeshie8
yes. keep going
anonymous
  • anonymous
976560 ?
ganeshie8
  • ganeshie8
correct ! gw :)
anonymous
  • anonymous
Thankyouu (: . ii need help on few more of these questions. 5. Jackie deposited $5 into a checking account in February. For each month following, the deposit amount was doubled. How much money was deposited in the checking account in the month of August?
ganeshie8
  • ganeshie8
March : 2 times April : 2^2 times May : 2^3 times June : 2^4 times July : 2^5 times Aug : 2^6 times
ganeshie8
  • ganeshie8
So, in August it wud be 5 x 2^6 = ?
anonymous
  • anonymous
soo 320 ?
ganeshie8
  • ganeshie8
yes
anonymous
  • anonymous
6. A local grocery store stacks the soup cans in such a way that each row has 2 fewer cans than the row below it. If there are 32 cans on the bottom row, how many total cans are on the bottom 14 rows?
ganeshie8
  • ganeshie8
use arithmetic series formula
ganeshie8
  • ganeshie8
first term, a = 32
ganeshie8
  • ganeshie8
common difference, d = -2
ganeshie8
  • ganeshie8
n = 14
ganeshie8
  • ganeshie8
\(Sn = \frac{n}{2}(2a + (n-1)d)\) = ?
anonymous
  • anonymous
use that equation ? ^^^^^
ganeshie8
  • ganeshie8
yes thats the sum formula for arithmetic series
ganeshie8
  • ganeshie8
give it a try
anonymous
  • anonymous
Sn=n/2(2a+(n-1)d) Sn=14/2(2(32)+(14-1)-2) Sn=7(64+13-2) Sn=7(75) Sn=525
ganeshie8
  • ganeshie8
Sn=n/2(2a+(n-1)d) Sn=14/2(2(32)+(14-1)(-2)) Sn=7(64+13(-2)) Sn=7(64-26) Sn= ?
anonymous
  • anonymous
Sn=7(64-26) Sn=7(38) Sn=190
ganeshie8
  • ganeshie8
Sn=7(64-26) Sn=7(38) Sn= ?
anonymous
  • anonymous
opps i mean 266
ganeshie8
  • ganeshie8
correct !
anonymous
  • anonymous
thankyou very much (: . i only have 3 more. 8. A fireplace contains 46 bricks along its bottom row. If each row above decreases by 4 bricks, how many bricks are on the 12th row? am i supposed to use the same formula ?
ganeshie8
  • ganeshie8
its arithmetic sequence but this time the question is not about finding sum
ganeshie8
  • ganeshie8
we need to find the 12th term
ganeshie8
  • ganeshie8
\(a = 46\) \(d = -4\) \(a_{12} = ?\)
ganeshie8
  • ganeshie8
use the nth term of arithmetic sequence formula : \(a_n = a + (n-1)d\)
anonymous
  • anonymous
so it is suppose 46n=46+(n-1)-4d to be
ganeshie8
  • ganeshie8
\(a_{12} = 46 + (12-1)(-4)\) = ?
anonymous
  • anonymous
a12=46+(12-1)(-4) a12=46+(11)(-4) a12=46+-44 a12=2
ganeshie8
  • ganeshie8
perfect !
anonymous
  • anonymous
yesss (:. ok last two ! 7. A major US city reports a 12% increase in decoration sales during the yearly holiday season. If decoration sales were 8 million in 1998, how much did the city report in total decoration sales by the end of 2004?
ganeshie8
  • ganeshie8
So, 1998 to 2004, thats how many years ?
anonymous
  • anonymous
6
ganeshie8
  • ganeshie8
good, n = 6
ganeshie8
  • ganeshie8
a = 8 million
ganeshie8
  • ganeshie8
12% increase => r = 1.12
anonymous
  • anonymous
so use the geometric sequence ?
ganeshie8
  • ganeshie8
sales in 2004 = \(\large ar^{6-1}\) = \(\large 8 (1.12)^{5}\) = ?
ganeshie8
  • ganeshie8
^ yes
anonymous
  • anonymous
ok i got Sn= a(1 - r^n) ------------- 1- r Sn= 8,000,000(1 - 1.12^6) ------------- 1- 1.12 Sn= 8,000,000(1 - 1.97) ------------- 1- 1.12 Sn= 8,000,000(-0.97) ------------- 1- 1.12 Sn= -7760000 ------------- 0.12
ganeshie8
  • ganeshie8
i think the question is oly asking about sales in 2004, so we dont have to find the sum of sales in all years
ganeshie8
  • ganeshie8
just find the sales in 2004, that wud be enough i guess
ganeshie8
  • ganeshie8
Since you found the Sum in all years already, lets finish it.
ganeshie8
  • ganeshie8
Sn= a(1 - r^n) ------------- 1- r Sn= 8,000,000(1 - 1.12^6) ------------- 1- 1.12 Sn= 8,000,000(1 - 1.97) ------------- 1- 1.12 Sn= 8,000,000(-0.97) ------------- 1- 1.12 Sn= -7760000 ------------- -0.12 = ?
anonymous
  • anonymous
Sn= -7760000 ------------- 0.12 -6466666 I ALSO DID the other formula Sales in 2004 ,,,, ar^6-1 8(1.12)^5 (8)1.76 14
anonymous
  • anonymous
was that right ? ^^^ last one . Using complete sentences, explain the difference between an exponential function and a geometric series.
ganeshie8
  • ganeshie8
both are right. see ur options and tick which ever exists
ganeshie8
  • ganeshie8
Sn= -7760000 ------------- -0.12 6466666
ganeshie8
  • ganeshie8
its a positive value
anonymous
  • anonymous
opps . i have to be careful with those signs.
ganeshie8
  • ganeshie8
:)
anonymous
  • anonymous
can you help with the last one ?
ganeshie8
  • ganeshie8
sure
anonymous
  • anonymous
Using complete sentences, explain the difference between an exponential function and a geometric series.
ganeshie8
  • ganeshie8
interesting q
anonymous
  • anonymous
all i know is geometric series is a formula.
ganeshie8
  • ganeshie8
Both exponential function and a geometric sequence increase exponentially. The only difference between them is that a geometric sequence is discrete, but an exponential function is defined everywhere. In other words, a geometric sequence is defined only for few values only, where as an exponential function is defined is smooth and defined everywhere.
ganeshie8
  • ganeshie8
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ganeshie8
  • ganeshie8
|dw:1371417346323:dw|
ganeshie8
  • ganeshie8
if u see, exponential function is continuous and smooth.
ganeshie8
  • ganeshie8
but the geometric sequence is breaking in between..
anonymous
  • anonymous
OMG . you are sooooooo Much helpp. I dont know were i would be without all your help !!!!!
ganeshie8
  • ganeshie8
its okay :) you're brilliant !

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