Find the nth term of the arithmetic sequence {an} whose initial term a and common difference d a

step 1 So in this problem, we're first being asked to write an equation that will allow us to find the

Find the nth term of the arithmetic sequence {an} whose...

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Key Concepts

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers in which each term is derived by adding a constant value, known as the common difference, to the preceding term. This concept is fundamental in sequences and series, allowing for predictable linear progressions, and is used in various applications including finance, computer science, and physics.

nth Term Formula

The nth term of an arithmetic sequence can be calculated using the formula a_n = a + (n - 1)d, where a represents the first term, d is the common difference, and n is the position of the term in the sequence. This formula is essential for directly finding any term in the sequence without having to list all preceding terms.

Application of the Formula

The ability to apply the nth term formula allows one to efficiently determine any specific term in an arithmetic sequence, particularly useful when the sequence extends to a large n-th term. This method streamlines problem-solving by eliminating the need for iterative computations of each term.

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