Question

. Find the sum of the geometric sequence. (1 point)

1, 1/2, 1/4, 1/8, 1/16.

Answer 1

@nincompoop any ideas?

Answer 2

ther is 2 formulas to find sum of geothermic sequence :
sum of finite geothermic seq. and sum of infinite geothermic seq.

Answer 3

The formula for the sum of finite geometric seq.
\[\huge\rm s_n = a_1 (\frac{ 1 -r^n }{ 1-r })\]
if r is less than one then use this formula for infinite geo seq.
\[\huge\rm s = \frac{ a_1 }{ 1-r }\]
^^^ if \[\left| r \right| < 1\]
r = ratio

Answer 4

Alright @Nnesha how would I use that

Answer 5

first find ratio

Answer 6

do you know how to find r ??

Answer 7

No

Answer 8

r is the common ratio of the sequence
you can find r by dividing next term with the previous one
\[\huge\rm r = \frac{ a_2 }{ a_1 } = \frac{ a_4}{ a_3}\] so on

Answer 9

\[a_1\] first term
\[a_2\] 2nd term

Answer 10

a geometric sequence is defined by some common value is multiplied each time to get the next value.

so: 1*r = 1/2 should tell us the value of r

Answer 11

yep that's right
to find ratio you cane either multiply or divide
both ways you will get same answer
for example 3 ,9 ,27
3 r = 9 to solve for r you have to DIVIDE both side by 9
so r =9/3 ~~~~ which is same as r =a_2/a_1