Question

Use the formula for the sum of the first n terms of a geometric sequence to solve. Find the sum of the first 8 terms of the geometric sequence: -8, -16, -32, -64, -128, . . . .

Answer 1

know the formula ?

Answer 2

no i dont know

Answer 3

@hartnn Help me solve it

Answer 4

\(\large S_n = a_1 \dfrac{r^n -1 }{r-1}\)

Answer 5

where a1 i s the first term = ...?
n = number of terms = 8 is given
r = common ratio = ....?
can u find ?

Answer 6

ok what is the common ratio

Answer 7

its the ratio of next term/ current term
r = 2nd term/1st term = 3rd term/2nd term = 4th term/3d term =.....
and so on

Answer 8

so whats r here ?

Answer 9

r is 8 right

Answer 10

no....
r = -16/-8 = 16/8 = ... ?

Answer 11

2

Answer 12

when i add them up all four after dividing =8

Answer 13

yes,
r=2
a1 = 1st term =-8
n=8
just plug these in the formula!

Answer 14

why did u add them up ?

Answer 15

if i dont add them up
they are all equal 2

Answer 16

did u get how r =2 now ?

Answer 17

yes

Answer 18

good, so use the formula, u have all the values now

Answer 19

you can pretty much just tell what the ratio is by looking at the sequence :)

Answer 20

i got as final answer \[S _{8}=-8\frac{ 2^{8}-1 }{ 2-1 }\]
\[S _{8}=-1024\]

Answer 21

how can i further simplify it

Answer 22

whats 2^8 =... ?

Answer 23

it was r^n right

Answer 24

yes
i am asking for the value :)
2^8 = 256 ,right ?

Answer 25

yes

Answer 26

so numerator = 256-1 =255
and you sum is just -8*255 =...

Answer 27

-2040

Answer 28

that would be correct sum :)

Answer 29

thnxs @hartnn

Answer 30

welcome ^_^