Question

Use the formula for S_n to find the sum of the first five terms of the geometric sequence

12,-4,4/3,-4/9,...

Answer 1

r = -4/12 = -1/3 a = 12
Sn = an - a
------
r - 1
tn = ar^n-1

We will first find tn, i.e. t5; the fifth term of the sequence.
t5 = 12(-1/3)^5-1
t5 = 12(-1/3)^4
t5 = 12(0.012345679)
t5 = 0.148

Now we can use the geometric series formula to find the sum of the first 5 terms.

Sn = 0.148 - 12
---------
(-1/3)-1
Sn = -11.852
--------
-1.33
Sn = 8.911

Therefore, the sum of the first 5 terms of the series is 8.911.

Answer 2

so u can see the pattern is dividing by negative three each time
12, -4, 4/3, -4/9, 4/27
now we have five terms just plus them altogether.
It turns out to be 9.037 and the 037 repeats.

Answer 3

That was incorrect. It was 244/27.

Answer 4

yeah so 9.037

Answer 5

yep

Answer 6

what about 03,-6,6/5,-6/5,..? I keep trying and get the wrong answer. dividing by -5 right?

Answer 7

wait the numbers are 3, -6, 6/5, -6/5 right?

Answer 8

-6/25 is the last one.

Answer 9

but it's not dividing by -5 because the first number is 3 and if 3 is divided by -5 it is -3/5 not -6 so it's not -5.

Answer 10

first number 30. sorry didnt see that mistake.

Answer 11

so it's the first five numbers will be 30, -6, 6/5, -6/25, 6/125 and so we just add them altogether to get 25.008.

Answer 12

thnx that makes sense:)

Answer 13

np :)