Question

geometric sequences problem help!

Answer 1

@jim_thompson5910 hey do you think you have the time to help me out on this? im lost on where to start!

Answer 2

What's the starting height?

Answer 3

30feet?

Answer 4

the only info i have is what is in the question

Answer 5

so the first term is 30. The next term is found by multiplying 0.6 by the previous term

30*0.6 = ??

Answer 6

so that would be 18

Answer 7

and then the next term after that is ??

Answer 8

10.8

Answer 9

you keep going, multiplying by 0.6 each time to generate the terms

Answer 10

oh and so then i continue to do that until im at the 5th term and that will be my answer?

Answer 11

correct

Answer 12

okay so i got 2.33. And that is all there is to the question?

Answer 13

it always seems so simple once i figure it out. hahaha thank you!

Answer 14

a shortcut is to use the nth term of a geometric sequence

that formula is

Tn = a*(r)^(n-1)

in this case, a = 30 and r = 0.6

so,

Tn = 30*(0.6)^(n-1)

now plug in n = 6

Tn = 30*(0.6)^(n-1)

T6 = 30*(0.6)^(6-1)

T6 = 2.3328

and you get the same answer

Answer 15

you're welcome

Answer 16

how did you determine it was .6 though instead of 60?

Answer 17

because the common ratio is 0.6

the common ratio is the number you multiply each previous term by to get the next term

Answer 18

30 --> 18 ( multiply by 0.6)

18 --> 10.8 (multiply by 0.6)

etc etc

Answer 19

yes i know that, but i was just wondering why you converted the 60 to .6 because in the question it says 60% but i think i get it. in this question, is the first term going to be 2,000,000?

Answer 20

oh, 60% = 0.60 in decimal form

Answer 21

60% = 60/100 = 0.60

Answer 22

and yes, the first term is 2 million

Answer 23

and so is the ratio .2? im not sure how that would work because if i continued to multiply it by .2 the number is going to get smaller and smaller

Answer 24

the ratio would be 1+0.2 = 1.2

Answer 25

his salary increases 20% each year, so that's the same as saying 120% = 1.2

Answer 26

120% = 100% + 20%

basically you add 20% to the existing 100% he's making previously to get the new 120%

Answer 27

ahhh okay. so then im multiplying by that 5 times to get the nth term. would the answer be A? 4.98?

Answer 28

to get the 5th term* not the nth.

Answer 29

hmm no it said that was wrong. did i maybe multiply once too much?

Answer 30

you went one step too far, yeah

Answer 31

first year: 2 million

second year: 2*1.2 = 2.4 million

third year: 2.4*1.2 = 2.88 million

fourth year: 2.88*1.2 = 3.456 million

fifth year: 3.456*1.2 = 4.1472 million

Answer 32

shortcut

Tn = 2*(1.2)^(n-1)

T5 = 2*(1.2)^(5-1)

T5 = 4.1472

Answer 33

ah okay yeah i see. thank you again!!