# Why Does Geometric Sequence General Term Formula Use n, Not n-1?

• L²Cc
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
L²Cc
do you have an explanation to why sometimes the general term formula for geometric sequence is not raised to n-1 but to simply n?

because you could have $$\sum_{n=0}^{\infty} ar^{n}$$ or $$\sum_{n=1}^{\infty} ar^{n-1}$$

Or $$\sum_{n=k}^{\infty} ar^{n-k}$$

Last edited:
oh ok...so from what I understood, if the sequence starts at zero then the formula raised to n because if it was n-1 then it will read -1, right?

that is correct

all right thank you!

## 1. Why does the geometric sequence general term formula use n instead of n-1?

The general term formula for a geometric sequence is given by an = a1rn-1, where an is the value at the nth term, a1 is the initial value, and r is the common ratio. The reason n is used instead of n-1 is because the exponent n-1 represents the number of terms before the nth term, while n represents the nth term itself. This is consistent with the definition of a geometric sequence, where the value at each term is obtained by multiplying the previous term by the common ratio r.

## 2. Can we use n-1 in the geometric sequence general term formula instead of n?

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 nth term. Using n-1 would result in an incorrect formula and would not accurately represent the sequence.

## 3. Does the value of n in the geometric sequence general term formula affect the outcome?

Yes, the value of n in the general term formula for a geometric sequence is crucial in determining the value at the nth 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 nth term.

## 4. Why is the value at the first term represented by a1 and not a0 in the geometric sequence general term formula?

The value at the first term in a geometric sequence is represented by a1 instead of a0 because the index of the first term in a sequence is typically denoted as 1, not 0. Furthermore, using a0 would result in an incorrect formula, as it would not accurately represent the sequence.

## 5. Can we use a different variable instead of n in the geometric sequence general term formula?

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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