Question

What is the sum of the geometric sequence 8, –16, 32 … if there are 15 terms?

Answer 1

Ooh well let's get the sequence first. What do you see is the pattern in here?

Answer 2

Times 2

Answer 3

no times -2

Answer 4

Close. It's not quite 2. How would we get from 8 to -16 and then back to 32?

Answer 5

Oh you got it

Answer 6

So now the only way I know how to do it is find multiply it all be -2

Answer 7

so that is 8,-16,32,-64,128,-256,512,-1024,2048,-4096,8192,-16384,32768,-65536,131072

Answer 8

the formula for the sum of n terms is

Sn = a * 1 - r^n
------
1 - r

Answer 9

I knew there was an easier way :) Thank you

Answer 10

a = first term, r = common ratio ( here = -2)

Answer 11

ok im going to try and work it out

Answer 12

Sn= a*1 - r^n
-------------
1- r

Sn= 8*1 - (-)2^n
-------------
1- (-)2


Sn= 8 + 2^n
-------------
3

Answer 13

thats what i got........ ?

Answer 14

Sn= a*1 - r^n
-------------
1- r

Sn= 8*1 - (-2)^n
-------------
1- (-2)

Answer 15

since you wanto find sum for 15 terms, put n = 15

Answer 16

ohh okk . one sec.

Answer 17

Sn= 8 + 2^15
-------------
3
Sn= 8 + 30
-------------
3
Sn= 38
-------------
3

Answer 18

not exactly...

Answer 19

2^15 means, 2 power 15

Answer 20

like this : \(2^{15}\)

Answer 21

Sn= a*1 - r^n
-------------
1- r

Sn= 8*1 - (-2)^n
-------------
1- (-2)

Sn= 8*1 - (-2)^15
-------------
1- (-2)

Sn= 8*1 + (2)^15
-------------
1 + (2)

Sn= 8*1 + 32768
-------------
3

Sn= 8*32769
-------------
3

Answer 22

see if u can take it from here

Answer 23

thats * not +

maybe my formula was ambiguous

i should have written it as

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

Answer 24

so its 8 * 32769
--------
3