Question

a package dropped from a helicopter falls 4.7m during the first second, 13.6m during the second, 22.5m during the third second and so on. how high is the helicopter if the package takes 10 seconds to reach the ground?

Answer 1

hint: arithmetic series

Answer 2

yes I found it to be arithmetic

Answer 3

I am stuck

Answer 4

do you know how to sum arithmetic series?

Answer 5

Sn=n/2[2a1+(n-1)d]

Answer 6

so can you identify \(a_1\), \(n\) and \(d\)?

Answer 7

a1=4.7 and n=10 d=8.9

Answer 8

yep, so now you can calculate answer yourself?

Answer 9

and to clarify this is what you write for sum formula?
\[S_n=\frac{2a_1+(n-1)d}{2}n\]
right?

Answer 10

I will do it then I will ask you to check

Answer 11

ok

Answer 12

first step: an=a1+(n-1)d
a10=4.7+(10-1)8.9=84.8

Answer 13

shouldnt it be 2a1?

Answer 14

did I use wrong formule

Answer 15

ah you calculating \(a_n\)? why?

Answer 16

second step:
Sn=n/2(a1+an)
Sn=10/2(4.7+84.8)
Sn=447.5

Answer 17

yeh you can do that way too and your answer is correct

Answer 18

how can i do it without calculating an?

Answer 19

you have written yourself:
Ocuane
Sn=n/2[2a1+(n-1)d]
21 minutes ago
so you can just plug in numbers but it's actually same but you could do in 1 step

Answer 20

just hard to judge which formule to use

Answer 21

its same formula

Answer 22

\[S_n=\frac{a_1+a_n}{2}n=\frac{a_1+a_1+(n-1)d}{2}n=\frac{2a_1+(n-1)d}{2}n\]

Answer 23

if you know \(a_n\) you can use first one but if you don't you can use second one without even evaluating \(a_n\)

Answer 24

so first I have to identify what i have to decide which formule to use am i right?

Answer 25

yeah but you can always use one formula it just save a bit of time

Answer 26

I tryed to plug in without calculating an and did not get the same result

Answer 27

try it again you should get same result

Answer 28

I tryed and got 127.1

Answer 29

show me

Answer 30

Sn=n/2[2a1+(n-1)d]
=10/2[2*4.7+(10-1)8.9]
=127.1

Answer 31

\[\frac{2\cdot4.7+(10-1)8.9}{2}10\]
did you write like ths?

Answer 32

no

Answer 33

so this is correct formula

Answer 34

do you understand now?

Answer 35

still doing it

Answer 36

yes got it had done calculations wrong thanks so much