Question

what is the common difference of a 57- arithmetic sequence where the 1st term is -25 and he sum is 17,727 ?

Answer 1

\[\LARGE S_{57}=\frac {57}{2}[2\cdot a_1+(57-1)d]\]
\[\LARGE 17727=\frac{57}{2}[2\cdot (-25)+56d]\]
find d (difference.)

Answer 2

d= 14535 ?

Answer 3

it can't be lol ... then a_1=-25
a_2=14515
a_3 ...
you have a_57=17727
that's impossible... try again :)

Answer 4

im confused

Answer 5

where are you confused...can you show how did you come up with d=14535 ? :)

Answer 6

im confused on how to get d

Answer 7

ok ... but do you mind showing what you've worked so far, so I can see where you got it wrong. ?

Answer 8

57/2 ( 2. a1 (56) d this is where i get confused

Answer 9

you have a1=-25
\[\LARGE 17727=\frac{57}{2}[-50+56d]\]
now multiply both sides by 2 and you'll get:
\[\LARGE 2\cdot 17727=57[-50+56d]\]
now divide both sides by 57 and you'll get:
\[\LARGE \frac{2\cdot 17727}{57}=-50+56d\]
now grab a calculator and calculate the left side and tell me what you get... so we can go further . ;)

Answer 10

622

Answer 11

d is 12

Answer 12

ok///

we have:
\[\LARGE 622=-50+56d\]
now add 50 to both sides
622+50=-50+50+56d
672=56d
now divide both sides by 56
and tell me what you get

Answer 13

yes d=12 well done...

Answer 14

thanks

Answer 15

My pleasure :)