Check please--- Geometric Sequences

hat is the sum of the first five terms of the geometric sequence in which a 1=20 and r=1/4

Question

Check please--- Geometric Sequences

hat is the sum of the first five terms of the geometric sequence in which a 1=20 and r=1/4

elise_a18 · Answer

I got 164.1406

afro · Answer

aren't you suppose to multiply the first by 1/4 which is the rate?

elise_a18 · Answer

I don't think that's the first step, I think raising 1/4 to the power of 5 is the first

afro · Answer

O_O why would you do that when you could just multiply 1/4 by 20

afro · Answer

and do it with each answer you get until you get to 5

elise_a18 · Answer

because I'm finding the partial sum of the first 5 terms

afro · Answer

is that what the question asked? or are you suppose to find the fifth term in the rule of geometric sequences

elise_a18 · Answer

I need to find the Sum of all the terms up until the fifth

afro · Answer

yea, well that's quicker, but how did you get that huge number

afro · Answer

multiply that decimal number to the 20

elise_a18 · Answer

instead of using just .25, i used 1.25 and raised it to the 5th power before subracting it from 1

elise_a18 · Answer

i was trying to learn from my last problem... :/

afro · Answer

something totally different the last problem you were dealing with a different formula

elise_a18 · Answer

I just don't know which formula to use... i did it again with another and got 26.64025

elise_a18 · Answer

@agent0smith @zarkam21

elise_a18 · Answer

@zepdrix  does 26.64.... seem right to you?

zepdrix · Answer

Probably >.<
I dunno I'm trying to remember the formula thingy

elise_a18 · Answer

|dw:1476940567725:dw|

zepdrix · Answer

I worked it out on paper, I think it's this for partial sum of geometric,$$\large\rm S_n=a_1\cdot\frac{1-r^n}{1-r}$$

zepdrix · Answer

$$\large\rm S_5=20\cdot\frac{1-r^5}{1-r}$$

zepdrix · Answer

Plugging in our rate as well,$$\large\rm S_5=20\cdot\frac{1-.25^5}{1-.25}$$

zepdrix · Answer

Which works out to 26.640625

yay good job \c:/

elise_a18 · Answer

yee, ok then it says to express the answer as an improper fraction

zepdrix · Answer

Oh ok.
Then I guess we'll have to leave the calculator out of this.
Back up to this point,$$\large\rm S_5=20\cdot\frac{1-.25^5}{1-.25}$$Use 1/4 instead of the decimal value,$$\large\rm S_5=20\cdot\frac{1-\frac14^5}{1-\frac14}$$And simplify from there.

elise_a18 · Answer

i don't know how u_u

agent0smith · Answer

I'm sure you can simplify some of it... at least the (1/4)^5 and the 1 - 1/4