For each arithmetic sequence described, find a1 and d and construct the sequence by stating the

step 1 Okay, so let's first note that we're given that our fifth term, so that's A5 is equal to 44, and

For each arithmetic sequence described, find a1 and d and...

Key Concepts

nth Term Formula

The nth term formula of an arithmetic sequence provides a way to calculate any term in the sequence using its position. The formula is given by a? = a? + (n - 1)d, where a? is the first term and d is the common difference. This formula is critical for describing the sequence in its general form and allows for quick computation of specific terms without listing the entire sequence.

Arithmetic Sequence

An arithmetic sequence is an ordered list of numbers in which the difference between consecutive terms is constant. This constant difference, known as the common difference, is added to each term to generate the next term in the sequence. The properties of arithmetic sequences allow for straightforward calculation of any term in the sequence, provided the first term and the common difference are known.

Common Difference

The common difference is the fixed amount added to each term of an arithmetic sequence to obtain the next term. It is a key parameter in the arithmetic sequence, and if two terms of the sequence are known, the common difference can be found by dividing the difference of these terms by the difference in their positions within the sequence.

First Term

The first term of an arithmetic sequence is the starting point from which every other term is derived using the common difference. Knowing the first term is essential for constructing the sequence and formulating its general term. It serves as the foundation in the formula for the nth term and is often determined using information provided about other terms in the sequence.

System of Equations

When given two specific terms of an arithmetic sequence, a system of equations can be set up using the general formula for the nth term to solve for unknowns like the first term and the common difference. This involves creating equations based on the positions of the given terms and their values, and then solving this system to find the values that satisfy both equations simultaneously.

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