Question

What is the sum of a 7–term geometric series if the first term is 6, the last term is 24,576, and the common ratio is –4?

Answer 1

Do you know the formula for the sum of the terms in a geometric sequence?

Answer 2

no idea -____- & btw i only have three questions today :D

Answer 3

There are two basic ways to do it

Answer 4

ohhh i googled it and the final answer is 19,662 lol

Answer 5

You can generate all 7 terms like so

6, -24, 96, -384, 1536, -6144, 24576

Note: multiply each number by -4 to get the next term

Then add them up

6+(-24)+96+(-384)+1536+(-6144)+24576 = 19662

Answer 6

lol jk i got that one too , now all i need is this last one -___-

At the end of the first day, 6 weeds appear in your neighborhood park. Each day, the number of weeds increases by four times. How many weeds will be in the park at the end of 14 days? Make sure to show your work.

Answer 7

OR

You can use the formula

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

S7 = 6*(1-(-4)^7)/(1-(-4) )

S7 = 19662

Answer 8

Either way, you get the same answer

Answer 9

okay thanks :) i dont have alota questions on that for the exam so idc , i just need to know how to do the word problem -___-

Answer 10

First day: 6 weeds

Second day: 6*4 =24 weeds

Third day: 24*4 =96 weeds

etc etc

So we have the following sequence

6, 24, 96, 384, 1536, 6144, 24576, 98304, 393216, 1572864, 6291456, 25165824, 100663296, 402653184

Answer 11

Add up the terms to get:

6+24+96+384+1536+6144+24576+98304+393216+1572864+6291456+25165824+100663296+402653184 = 536870910

Answer 12

Alternatively...


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


S14 = 6*(1-4^14)/(1-4)


S14 = 536870910


which gives you the same answer

Answer 13

I'd use the formula to save time, but it helps to see all the terms added up so you know that the formula is working (and how it's working)

Answer 14

thank you sooo muchhhh :) brb !

Answer 15

you're welcome