Question

Find the sum of the geometric sequence.

Answer 1

1/4, 1/16, 1/64, 1/256

Answer 2

I don't know where to start

Answer 3

it's geometric sequence firs step to find ratio
you can find ratio \[\huge\rm r = \frac{ a_2 }{ a_1} , \frac{ a_4 }{ a_3 }\]
divide next term by one previous one to get ratio

Answer 4

there are two formulas to find sum of geometric sequence
one is infinite geometric sequence
and 2nd one is finite geometric sereies
use this formula for infinite geometric when \[\left| r \right| <1\]\[\huge\rm s_n = \frac{ a_1 }{ 1-r }\]
and if ratio is greater than then apply this formula finite geometric series \[\huge\rm s_n = a_1 (\frac{ 1 - r^n }{ 1-r })\]

Answer 5

ok so r= 1/4

Answer 6

yes that's right which is less than one so you suppose to find finite or infinite geometric sum ??

Answer 7

infinite geometric sum

Answer 8

yep right a_1 first term
r= ratio :-) solve that

Answer 9

ok so 1/1-(1/4) = 4/3?
the first term is 1, I accidently started in 1/4

Answer 10

first term is 1 ???

Answer 11

yes

Answer 12

1/4, 1/16, 1/64, 1/256
first term is what ??

Answer 13

it goes 1, 1/4, 1/16...

Answer 14

I typed it in wrong at the beginning. I forgot to put one first

Answer 15

ohh okay

Answer 16

so what do I do with 4/3 next

Answer 17

\[\huge\rm \frac{ 1 }{ 1 - \frac{ 1 }{ 4 } }\]
= 4/3 yes done

Answer 18

one of the options is 341/256. That's the same thing right?

Answer 19

hmmm not sure what are other options ?

Answer 20

341
1/192
1/768

Answer 21

yep that's the only one make sense to me

Answer 22

Yeah it makes sense to me too. Thank you @Nnesha

Answer 23

np :-)