Question

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?

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

Sn= a(1 - r^n)
-------------
1- r

Sn= 11(1 - (-4)^6)
-------------
1- (-4)

Sn= 11(1 - (4096))
-------------
5

Sn= 11(-4095)
-------------
5

Answer 5

99099 ?

Answer 6

im getting -9009

Answer 7

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 ?

Answer 8

we need to find r first

Answer 9

\(a_8 = 10 \times r^7 = 781250\)

=>

\( r^7 = 78125\)

\(r = 5\)

Answer 10

Now try to find the sum using the usual sum formula

Answer 11

one sec .

Answer 12

yo

Answer 13

im sorry . are you here @ganeshie8 ?

Answer 14

yea

Answer 15

its okay :)

Answer 16

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 ?

Answer 17

yes. keep going

Answer 18

976560 ?

Answer 19

correct ! gw :)

Answer 20

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?

Answer 21

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

Answer 22

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

Answer 23

soo 320 ?

Answer 24

yes

Answer 25

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?

Answer 26

use arithmetic series formula

Answer 27

first term, a = 32

Answer 28

common difference, d = -2

Answer 29

n = 14

Answer 30

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

= ?

Answer 31

use that equation ? ^^^^^

Answer 32

yes thats the sum formula for arithmetic series

Answer 33

give it a try

Answer 34

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

Answer 35

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= ?

Answer 36

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

Answer 37

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

Answer 38

opps i mean 266

Answer 39

correct !

Answer 40

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 ?

Answer 41

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

Answer 42

we need to find the 12th term

Answer 43

\(a = 46\)
\(d = -4\)

\(a_{12} = ?\)

Answer 44

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

Answer 45

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

Answer 46

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

Answer 47

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

Answer 48

perfect !

Answer 49

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?

Answer 50

So, 1998 to 2004, thats how many years ?

Answer 51

6

Answer 52

good, n = 6

Answer 53

a = 8 million

Answer 54

12% increase => r = 1.12

Answer 55

so use the geometric sequence ?

Answer 56

sales in 2004 = \(\large ar^{6-1}\)

= \(\large 8 (1.12)^{5}\)

= ?

Answer 57

^ yes

Answer 58

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

Answer 59

i think the question is oly asking about sales in 2004, so we dont have to find the sum of sales in all years

Answer 60

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

Answer 61

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

Answer 62

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

= ?

Answer 63

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

Answer 64

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

Answer 65

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

Answer 66

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

Answer 67

its a positive value

Answer 68

opps . i have to be careful with those signs.

Answer 69

:)

Answer 70

can you help with the last one ?

Answer 71

sure

Answer 72

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

Answer 73

interesting q

Answer 74

all i know is geometric series is a formula.

Answer 75

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.