Question

Which of the following gives a recursive representation with n > 2 of the partial sum of the geometric series below?
4 + 8 + 16 + 32.....

A. Sn = 4 + 2Sn-1
B. Sn = 4 + (1/2)Sn-1
C. Sn = 4 + Sn-1
D. Sn = 2Sn-1

Answer 1

@Annie7077 help?

Answer 2

what is Sn

Answer 3

S small n

Answer 4

whatever that means

Answer 5

It's the nth partial sum

Answer 6

I think the best way to do this is to just check each option

Answer 7

For instance, option D

S1 = 4
S2 = 4+8 = 12

notice how S2 is NOT equal to 2*S1, so option D is out

Answer 8

ok where is n in this equatio?

Answer 9

n refers to the index number of each term (n = 1 is the first term, n = 2 is the second, etc)

Answer 10

yes but where is it in this equation? where to substitute it in?

Answer 11

S1 is found by adding the first term. Basically S1 is the first term itself

Answer 12

S2 is found by adding the first two terms

S2 = 4+8 = 12

Answer 13

S3 is found by adding the first three terms

S3 = 4+8+16 = 28

Answer 14

etc etc

Answer 15

hopefully you see why D is false?

Answer 16

@jim_thompson5910 so a?

Answer 17

let's find out

Answer 18

S2 = 4 + 2S1

12 = 4 + 2*4

12 = 12 ... works

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S3 = 4 + 2*S2

28 = 4 + 2*12

28 = 28 ... works

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It turns out the others work as well, so you are correct

Answer 19

I put that last statement in because there is no upper limit on what to check, so you'd be at it forever.

Answer 20

@jim_thompson5910 thank you!

Answer 21

you're welcome