Question

−6 + 12 − 24 + 48 − 96 + ...
Is this a geometric series?

If it is a geometric series, what's the next term?

If it is a geometric series, give the ratio between successive terms

Answer 1

yeah

Answer 2

-2

Answer 3

next term is192

Answer 4

can you explain the formula?

Answer 5

yeah second term / first term gives ratio

Answer 6

multiply ratio in last term you'll get next term

Answer 7

YOu have to ask yourself: can I find a constant number to multiply each term with, so that it gives the next one?
If there is such a number, the sequence is geometric

Answer 8

so its -2

Answer 9

so if its a constant number means that the sequence is geometric?

Answer 10

Yes!

Answer 11

Every time, multiply with the same number to get the next term. That is a geometric sequence.

Answer 12

no not necessary

Answer 13

there are different types of series like AP and Gp .........

Answer 14

whats AP and Gp?

Answer 15

here if you ask for gp then common ratio (which can be both variable or constant ) is multiplied or divided to get the series

Answer 16

AP is Arithmetic Progression and GP is geometric progression

Answer 17

here you are dealing with gp

Answer 18

like e.g. A.P.- 2,4,6,8............
G.P.- 3,6,9,.........

Answer 19

for example if i have
y^2 + y^3 + y^4 + y^5 + ...

Is this a geometric series?

Answer 20

yeah

Answer 21

here y is multiplied in each term to get next term

Answer 22

thank you for your help

Answer 23

mention not

Answer 24

what about this series:

6+6(0.1)+6(0.1)^2+...6(0.1)^25

Answer 25

How many terms are being added?

Answer 26

here you have formula for gp series

Answer 27

Same as counting from 0..25

Answer 28

So that would be 26 terms...

Answer 29

t= a(1-r^n/1-r) where r is common ratio and n is no. of term you can put t as last term given and calculate for n . this formula works only when r<1

Answer 30

if r>1 then exchange r and 1

Answer 31

wait why is it 26 terms?

Answer 32

hey I gave you formula try that youll know

Answer 33

what's "a" in the formula?

Answer 34

how did you get the formula?

Answer 35

i'm sorry for asking so many questions :(

Answer 36

a is first term

Answer 37

nevermind for question i am happy you are asking

Answer 38

try it and do tell me if you get problem

Answer 39

alright thanks

Answer 40

mention not

Answer 41

so for "n" in this series is 26?

Answer 42

i dont know didn calculate if thats what u r getting then yes

Answer 43

the "n" in the formula is the number of term you so the number if terms in this serie is 26?

Answer 44

yeah

Answer 45

is the common ratio 0.1?

Answer 46

it is right?

Answer 47

Ill have to calculate but i am really sorry i cant cuz its nighttime here nad no lights and paper to work on

Answer 48

don't worry about it

Answer 49

can you help me with another series?

Answer 50

yeah feel free

Answer 51

Hey If you ever need help in mathematics or any science subject just drop me mail on chauhanbhimesh23@gmail.com and do leave reference.......i'm a bit forgetful person

Answer 52

Ill contact you ASAP

Answer 53

the series is

3-1+(1/3)-(1/9)+(1/27)-(1/81)+...

Answer 54

I know the ratio is -1/3

Answer 55

but what formula do I use to find the exact sum?

Answer 56

the formula for sum is s= a (1-r^n/1-r)

Answer 57

but this is a infinite geometric series. what do i put for "n"?

Answer 58

ohk then use this s= a/1-r

Answer 59

youll get the answer

Answer 60

thanks

Answer 61

my pleasure

Answer 62

where you from?

Answer 63

india

Answer 64

how old are you?

Answer 65

17

Answer 66

applied to MIT this year just waiting for results

Answer 67

hopefully you get in

Answer 68

maybe maybe not

Answer 69

I'm Mexico I applied to Yale but I didn't get in

Answer 70

:(