Find the fifth term and the nth term of the geometric sequence whose initial term a1 and common

step 1 Suppose we have a sequence where the first term, A1, is the square root of 2, and the common rat

Find the fifth term and the nth term of the geometric...

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Key Concepts

Geometric Sequence

A geometric sequence is a list of numbers where each term after the first is obtained by multiplying the preceding term by a constant called the common ratio. This multiplicative process distinguishes geometric sequences from arithmetic sequences, which add a constant difference to get the next term.

Initial Term

The initial term, typically denoted as a?, is the first term of a sequence. It serves as the starting point or base value from which subsequent terms are generated by repeated multiplication by the common ratio.

Common Ratio

The common ratio, represented by r, is the constant factor by which each term in a geometric sequence is multiplied to produce the next term. It determines whether the sequence grows, decays, or oscillates, depending on its value.

Nth Term Formula

The nth term of a geometric sequence can be calculated using the formula a? = a? · r^(n?1). This formula encapsulates the relationship between the sequence’s initial term, common ratio, and the number of terms, enabling the computation of any term within the sequence.

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