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L²Cc
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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?
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.
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.
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.
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.
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.