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?

- anonymous

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- 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

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

hint : (-4)^6 = 4^6 = 4096

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## More answers

- 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

99099 ?

- ganeshie8

im getting -9009

- 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

we need to find r first

- ganeshie8

\(a_8 = 10 \times r^7 = 781250\)
=>
\( r^7 = 78125\)
\(r = 5\)

- ganeshie8

Now try to find the sum using the usual sum formula

- anonymous

one sec .

- ganeshie8

yo

- anonymous

im sorry . are you here @ganeshie8 ?

- ganeshie8

yea

- ganeshie8

its okay :)

- 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

yes. keep going

- anonymous

976560 ?

- ganeshie8

correct ! gw :)

- 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

March : 2 times
April : 2^2 times
May : 2^3 times
June : 2^4 times
July : 2^5 times
Aug : 2^6 times

- ganeshie8

So, in August it wud be 5 x 2^6 = ?

- anonymous

soo 320 ?

- ganeshie8

yes

- 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

use arithmetic series formula

- ganeshie8

first term, a = 32

- ganeshie8

common difference, d = -2

- ganeshie8

n = 14

- ganeshie8

\(Sn = \frac{n}{2}(2a + (n-1)d)\)
= ?

- anonymous

use that equation ? ^^^^^

- ganeshie8

yes thats the sum formula for arithmetic series

- ganeshie8

give it a try

- 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

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

Sn=7(64-26)
Sn=7(38)
Sn=190

- ganeshie8

Sn=7(64-26)
Sn=7(38)
Sn= ?

- anonymous

opps i mean 266

- ganeshie8

correct !

- 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

its arithmetic sequence but this time the question is not about finding sum

- ganeshie8

we need to find the 12th term

- ganeshie8

\(a = 46\)
\(d = -4\)
\(a_{12} = ?\)

- ganeshie8

use the nth term of arithmetic sequence formula :
\(a_n = a + (n-1)d\)

- anonymous

so it is suppose
46n=46+(n-1)-4d to be

- ganeshie8

\(a_{12} = 46 + (12-1)(-4)\)
= ?

- anonymous

a12=46+(12-1)(-4)
a12=46+(11)(-4)
a12=46+-44
a12=2

- ganeshie8

perfect !

- 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

So, 1998 to 2004, thats how many years ?

- anonymous

6

- ganeshie8

good, n = 6

- ganeshie8

a = 8 million

- ganeshie8

12% increase => r = 1.12

- anonymous

so use the geometric sequence ?

- ganeshie8

sales in 2004 = \(\large ar^{6-1}\)
= \(\large 8 (1.12)^{5}\)
= ?

- ganeshie8

^ yes

- 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

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

just find the sales in 2004, that wud be enough i guess

- ganeshie8

Since you found the Sum in all years already, lets finish it.

- 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

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

was that right ? ^^^ last one . Using complete sentences, explain the difference between an exponential function and a geometric series.

- ganeshie8

both are right. see ur options and tick which ever exists

- ganeshie8

Sn= -7760000
-------------
-0.12
6466666

- ganeshie8

its a positive value

- anonymous

opps . i have to be careful with those signs.

- ganeshie8

:)

- anonymous

can you help with the last one ?

- ganeshie8

sure

- anonymous

Using complete sentences, explain the difference between an exponential function and a geometric series.

- ganeshie8

interesting q

- anonymous

all i know is geometric series is a formula.

- 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

|dw:1371417247668:dw|

- ganeshie8

|dw:1371417346323:dw|

- ganeshie8

if u see, exponential function is continuous and smooth.

- ganeshie8

but the geometric sequence is breaking in between..

- anonymous

OMG . you are sooooooo Much helpp. I dont know were i would be without all your help !!!!!

- ganeshie8

its okay :) you're brilliant !

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