Question

Please help! I will fan+medal
The nth term of a geometric sequence is given by an=27(0.1)^n-1

What are the first five terms of the sequence?

What is the sum of the first 10 terms of the sequence?

Answer 1

have you covered geometric sequences yet?

Answer 2

yes I believe the first 5 terms are 27, 2.7, 0.27, 0.027, and 0.0027

Answer 3

is that correct?

Answer 4

yeap

Answer 5

to get the sum of the first 10 terms
we'd use the "sum of a finite geometric sequence" formula thus \(\large \bf a_{\color{brown}{ n}}=27({\color{blue}{ 0.1}})^{{\color{brown}{ n}}-1}\qquad

S_{\color{brown}{ n}}=a_1\left(\cfrac{1-{\color{blue}{ r}}^{\color{brown}{ n}}}{1-{\color{blue}{ r}}}\right)\)

Answer 6

so the get the " S "um of the 10 terms just set n = 10

Answer 7

i got 10.46 as my answer

Answer 8

is that correct?

Answer 9

hmmm

Answer 10

\(\bf \large {
a_{\color{brown}{ n}}=27({\color{blue}{ 0.1}})^{{\color{brown}{ n}}-1}\qquad

S_{\color{brown}{ n}}=a_1\left(\cfrac{1-{\color{blue}{ r}}^{\color{brown}{ n}}}{1-{\color{blue}{ r}}}\right)
\\ \quad \\
S_{\color{brown}{ 10}}=27\left(\cfrac{1-{\color{blue}{ 0.1}}^{\color{brown}{ 10}}}{1-{\color{blue}{ 0.1}}}\right) }\) I seem to get something a bit bigger

Answer 11

https://www.google.com/search?client=opera&q=how+many+grams+in+1lb&sourceid=opera&ie=utf-8&oe=utf-8&channel=suggest&gws_rd=ssl#channel=suggest&q=27*(1-0.1%5E(10))%2F(1-0.1)

Answer 12

hmm so my answer is 29.9?

Answer 13

yeap

Answer 14

it can easy round to 30.. but yes.. 29.999999997

Answer 15

can you help me out with a few more questions?

Answer 16

sure... just post anew... if I dunno someone else may know, and we can also revuse each other

Answer 17

Okay ill close this and post a new one