OpenStudy (anonymous):

I have a small assignment to do for Algebra II. The topic is Geometric Series and I have a couple different questions... Please help!

4 years ago
OpenStudy (anonymous):

For problems 1 – 4, solve. You must show your work to receive credit. What is the sum of the geometric sequence 8, –16, 32 … if there are 15 terms? (1 point) What is the sum of the geometric sequence 4, 12, 36 … if there are 9 terms? (1 point) What is the sum of a 6-term geometric sequence if the first term is 11, the last term is –11,264 and the common ratio is –4? (1 point) What is the sum of an 8-term geometric sequence if the first term is 10 and the last term is 781,250? (1 point)

4 years ago
OpenStudy (anonymous):

@hartnn @nincompoop @campbell_st

4 years ago
OpenStudy (campbell_st):

well for a geometric series and the common ratio is greater then plus or minus 1 the sum is \[S_{n} = \frac{a(1 - r^n)}{1 - r}\] n = number of terms, a = 1st term and r = common ratio. the common ratio is found by comparing terms \[\frac{a_{2}}{a_{1}} = \frac{a_{3}}{a_{2}} ..... \] or is each term being multiplied by the same value. for the last question you'll need to find the common ratio using the formula for a term in a common ratio \[a_{n} = a_{1}r^{n -1}\] hope this helps

4 years ago
OpenStudy (anonymous):

@campbell_st can you please walk me through one of them? I have the formula written down and I plugged in A and N, but how do I find the common ratio?

4 years ago
OpenStudy (campbell_st):

ok... so in the 1st question the 1st term is a = 8 what was 8 multiplied by to get -16..?

4 years ago
OpenStudy (anonymous):

-2

4 years ago
OpenStudy (campbell_st):

yes ... and to check is the 3rd term -16 x -2 ...?

4 years ago
OpenStudy (anonymous):

32

4 years ago
OpenStudy (anonymous):

yes, it is

4 years ago
OpenStudy (campbell_st):

so you now have the common ratio, r = -2 substituting you get \[S_{15} = \frac{8(1 - (-2)^{15})}{1 - (-2)}\] all you need to do is take care with the negatives... and you'll get the sum

4 years ago
OpenStudy (anonymous):

so it's S15=-87381.33?

4 years ago
OpenStudy (anonymous):

wait... would it be 10,923?

4 years ago
OpenStudy (campbell_st):

well i got 87384

4 years ago
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