- #1

L²Cc

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In summary, the general term formula for a geometric sequence uses n instead of n-1 because n represents the nth term while n-1 represents the number of terms before the nth term. This is consistent with the definition of a geometric sequence where each term is obtained by multiplying the previous term by the common ratio. Using n-1 instead of n would result in an incorrect formula. The value of n in the formula is crucial in determining the value at the nth term, as it represents the number of terms in the sequence. The first term is represented by a1 instead of a0 because the index of the first term is typically denoted as 1, and using a0 would result in an incorrect formula. It is also possible to

- #1

L²Cc

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- #2

courtrigrad

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because you could have [tex] \sum_{n=0}^{\infty} ar^{n} [/tex] or [tex] \sum_{n=1}^{\infty} ar^{n-1} [/tex]

Or [tex] \sum_{n=k}^{\infty} ar^{n-k} [/tex]

Or [tex] \sum_{n=k}^{\infty} ar^{n-k} [/tex]

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- #3

L²Cc

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- #4

courtrigrad

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that is correct

- #5

L²Cc

- 149

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all right thank you!

The general term formula for a geometric sequence is given by **a _{n} = a_{1}r^{n-1}**, where

No, the use of **n** instead of **n-1** in the general term formula for a geometric sequence is necessary in order to correctly express the number of terms before the *n*^{th} term. Using **n-1** would result in an incorrect formula and would not accurately represent the sequence.

Yes, the value of **n** in the general term formula for a geometric sequence is crucial in determining the value at the *n*^{th} term. As **n** increases, the value of the term also increases, as it represents the number of terms in the sequence. Changing the value of **n** will result in a different value for the *n*^{th} term.

The value at the first term in a geometric sequence is represented by **a _{1}** instead of

Yes, we can use a different variable instead of **n** in the general term formula for a geometric sequence, as long as it is used consistently throughout the formula. Some common alternatives to **n** are **k**, **m**, or **t**, but any letter or symbol can be used as long as it is clearly defined. However, using **n** is the most common and accepted convention in mathematics.

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