Question

The nth term is a geometric sequence is given by
a(n)=3(.5)^(n-1)
take me step by step please and thank you
I need the first five terms

Answer 1

what's the question?

Answer 2

i need the first five terms, well i need help on how to do that

Answer 3

start with n=1 as the first term. For n=1 the value will be: \[\frac{3}{2^{0}} = 3\]
Can you try for the next term, n=2?

Answer 4

1.5?

Answer 5

good answer!

Answer 6

so its the right answer?

Answer 7

every term will be 1/2 times the previous term

Answer 8

yes by good i mean right

Answer 9

okay I also need to find the fifth partial sum i could add them all but i know there is like an actual way to do it can you help me with that?

Answer 10

basically u take the equation and plug in 0-4 into you n 0 being your first term and 4 being your last term

Answer 11

ummm no, i don't understand that

Answer 12

for your first term u would take the equation a3(.5)^(n-1) and where the n is u plug in 0, giving you your first term. then u do it again this time pluging in 1 which will equal your second term. you repeat until you have a total of 5 terms and since you are including zero u only need to plug in the number 0,1,2,3,4

Answer 13

oh okay but how do i find partial sums

Answer 14

yes there is a formula for the partial sum: \[3\frac{1-0.5^{n-1}}{0.5}\]

Answer 15

okay so for the fifth partial sum i put in 5 for n?

Answer 16

yes that is correct

Answer 17

the formula is \[a(1-r^n)/1-r\]

Answer 18

yea 5 for n and a would be your first term, and your r would be your rate

Answer 19

1.875? is this correct

Answer 20

no umm 5.625? is that the answer?

Answer 21

yes I am getting
5.625

Answer 22

yay!!!! thank you thank you! you are like a full bottle of awesome sauce!

Answer 23

Please note that what you and me have been discussing assumes that the first terms are for n=1, 2, 3, 4, 5. (not n=0,1,2,3,4)

Answer 24

My pleasure!