Two terms of an arithmetic sequence are given in each problem. Find the general term of the sequ

step 1 Okay, so we want to find a 16. So note that we're given our fifth term and our 11th term. So why

Two terms of an arithmetic sequence are given in each...

Key Concepts

Evaluating Specific Terms

Once the values of a? and d are found, the general term formula can be used to evaluate any specific term in the sequence by substituting the appropriate position number for n. This process is the final step in applying the foundational concepts of arithmetic sequences to specific problems.

Solving Systems to Find Sequence Parameters

When two specific terms of an arithmetic sequence are provided, setting up equations using the general term formula for each allows one to create a system of linear equations. Solving this system enables the determination of the first term and the common difference, which are crucial for further analysis or computation of other terms.

Arithmetic Sequence

An arithmetic sequence is a sequence of numbers where each term after the first is obtained by adding a constant value, known as the common difference, to the previous term. This concept is fundamental in understanding linear relationships in sequences.

Common Difference

The common difference is the constant amount by which each term in an arithmetic sequence increases or decreases. Determining this difference is essential for constructing the general formula of the sequence.

General Term Formula

The general term of an arithmetic sequence is expressed as a? = a? + (n - 1)d, where a? is the first term, d is the common difference, and n represents the term number. This formula allows one to compute any term in the sequence once a? and d are known.

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