Question

Evaluate the summation of 20 times 0.5 to the n minus 1 power, from n equals 3 to 12..

Answer 1

\(\bf {\huge \Sigma}_{{\color{brown}{ n}}=3}^{12}\quad a_1\cdot r^{{\color{brown}{ n}}-1}\implies a_1\left(\cfrac{1-r^{\color{brown}{ n}}}{1-r}\right)\)

Answer 2

can you explain further my level of confusion is insane @jdoe0001

Answer 3

well... \(\bf a_1 = 20\ and \ r=0.5\)
\(\bf a_1=\textit{1st term of sequence}\quad r=\textit{common ratio or "multiplier"}\)

Answer 4

okay so what is the first term of sequence??

Answer 5

so... what you have is pretty much... includes the 1st term and the common ratio
thus \(\bf {\huge \Sigma}_{{\color{brown}{ n}}=3}^{{\color{blue}{ 12}}}\quad 20\cdot 0.5^{{\color{brown}{ n}}-1}\implies (20\cdot 0.5^{{\color{brown}{ 3}}-1})\left(\cfrac{1-0.5^{\color{brown}{ {\color{blue}{ 12}}}}}{1-0.5}\right)\)

Answer 6

the 1st term... .in the sequence is 20
HOWEVER
you're asked to start adding from the n = 3, or 3rd term
thus I used \(\bf (20\cdot 0.5^{{\color{brown}{ 3}}-1})\)

Answer 7

okay so what is next

Answer 8

get the summation :)

Answer 9

how
???/

Answer 10

\(\bf {\huge \Sigma}_{{\color{brown}{ n}}=3}^{{\color{blue}{ 12}}}\quad 20\cdot 0.5^{{\color{brown}{ n}}-1}
\\ \quad \\
\implies \Large (20\cdot 0.5^{{\color{brown}{ 3}}-1})\left(\cfrac{1-0.5^{\color{brown}{ {\color{blue}{ 12}}}}}{1-0.5}\right)\)

Answer 11

9.99

19.95

29.98

39.96
so how do i get to one of these

Answer 12

well.... what did you get for the one above?

Answer 13

if you need a calculator https://www.desmos.com/calculator

Answer 14

thats the thing idk how to solve it.. im bad at math and my mom cant help me right now... so i have 0 clue what im doing with this

Answer 15

hmm well.. the idea is that you have to calculate the value so....

Answer 16

say for example.... what does \(\bf (20\cdot 0.5^{{\color{brown}{ 3}}-1})\) give you?

Answer 17

1.5

Answer 18

hm..... may want to recheck it

Answer 19

5

Answer 20

so.... 5 yes try now just the numerator of the fracton :)

Answer 21

.9997

Answer 22

yeap and the bottom will be 1-0.5 which is just 0.5

so just do a 5 * 0.9997 / 0.5 :)

Answer 23

9.997 OMG THANK YOU SO MUCHHHHH

Answer 24

yw