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Mathematics 93 Online
OpenStudy (anonymous):

1) How do you find the common ratio in a geometric sequence? 2) What is the formula for the nth term of a geometric sequence? 3) What is the formula for the sum of a finite geometric series? 4) What is the difference between an arithmetic and geometric sequence? 5) Why must the first term of a geometric sequence be nonzero?

OpenStudy (anonymous):

tell me first what is a geometric sequence????

OpenStudy (anonymous):

not exactly sure..has to do with a common ratio

OpenStudy (anonymous):

Sequences of numbers that follow a pattern of multiplying a fixed number from one term to the next are called geometric sequences. The following sequences are geometric sequences: Sequence A: 1 , 2 , 4 , 8 , 16 , ... Sequence B: 0.01 , 0.06 , 0.36 , 2.16 , 12.96 , ... Sequence C: 16 , -8 , 4 , -2 , 1 , ... For sequence A, if we multiply by 2 to the first number we will get the second number. This works for any pair of consecutive numbers. The second number times 2 is the third number: 2 × 2 = 4, and so on. For sequence B, if we multiply by 6 to the first number we will get the second number. This also works for any pair of consecutive numbers. The third number times 6 is the fourth number: 0.36 × 6 = 2.16, which will work throughout the entire sequence. Sequence C is a little different because it seems that we are dividing; yet to stay consistent with the theme of geometric sequences, we must think in terms of multiplication. We need to multiply by -1/2 to the first number to get the second number. This too works for any pair of consecutive numbers. The fourth number times -1/2 is the fifth number: -2 × -1/2 = 1.

OpenStudy (anonymous):

The terms of a geometric series form a geometric progression, meaning that the ratio of successive terms in the series is constant

OpenStudy (anonymous):

ok got it

OpenStudy (anonymous):

nth term \[ar ^{n-1}\]

OpenStudy (anonymous):

a-first term of sequence r-common ratio n-no. of terms in sequence

OpenStudy (anonymous):

ok i understand everything but #5

OpenStudy (anonymous):

IF THE FIRST TERM IS ZERO WHAT DO YOU THINK THE RATION OF SECOND AND FIRST TERM?

OpenStudy (anonymous):

Oops. Capslock

OpenStudy (anonymous):

0?

OpenStudy (anonymous):

Yes! If the ratio is zero, it won't become a geometric series, wouldn't it?

OpenStudy (anonymous):

Essentially geometric series is just multiplied by ratio again and again. If the ratio is zero, everything will be zero.

OpenStudy (anonymous):

The first term of a geometric series can't be 0 because then the following terms would have a ratio of 0 which isn't possible for a geometric sequence. is that ok?

OpenStudy (anonymous):

No no no. sorry. if the first term is zero. The ratio will be \[\frac{second term}{0}=error\]

OpenStudy (anonymous):

You get it?

OpenStudy (anonymous):

hmmm

OpenStudy (anonymous):

Everything divided by zero is error

OpenStudy (anonymous):

ooooohhh

OpenStudy (anonymous):

Now give me a best response and close the question! ;D

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