Here are the essential concepts you must grasp in order to answer the question correctly.
Geometric Sequence
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the sequence 2, 6, 18, 54, the common ratio is 3. Understanding geometric sequences is essential for applying the formula for the sum of their terms.
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Geometric Sequences - Recursive Formula
Sum of the First n Terms
The sum of the first n terms of a geometric sequence can be calculated using the formula S_n = a(1 - r^n) / (1 - r), where S_n is the sum, a is the first term, r is the common ratio, and n is the number of terms. This formula allows for efficient calculation of the total when dealing with a finite number of terms in a geometric series.
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Sigma Notation
Sigma notation is a concise way to represent the sum of a sequence of terms. It uses the Greek letter sigma (Σ) to indicate summation, specifying the index of summation, the starting and ending values, and the expression to be summed. In the given question, sigma notation is used to denote the sum of the terms generated by the formula 5^i from i=1 to i=6.
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