įinally, we can determine the eighteenth term in the sequence by substituting 𝑛 = 1 8 to find The general term for the given arithmetic sequence, using the commonĭifference 𝑑 = 3 and first term 𝑇 = 4 , is Therefore, the first term of the sequence is 𝑇 = 4 . Since we know that 𝑇 = 1 9 , we can substitute this into the formula to obtain Now, we can determine the first term by substituting 𝑛 = 6 and 𝑑 = 3 into this formula: Recall that the explicit formula for the 𝑛 t h term of an arithmetic sequence can be written in terms of the common difference Therefore, this must be an arithmetic sequence with common difference 3. Recall that an arithmetic sequence is defined byĪ constant common difference, 𝑑, between any two consecutive terms. We can see that each successive term can be obtained from the previous one by adding a common difference ( + 3). Now, let’s consider an example where we determine the general term from a table with values starting from the sixth term and then evaluate Hence, the general term of the sequence is 𝑇 = 2 𝑛 − 9 . The general term for the given arithmetic sequence, using the common difference 𝑑 = 2 and first term 𝑇 = − 7 , is Thus, we have a common difference 𝑑 = 2, which confirms that we have an arithmetic sequence. Let’s first calculate the difference between consecutive terms: We are given the first few values of the sequence, 𝑇, 𝑇, 𝑇, 𝑇 . The explicit formulaįor the 𝑛 t h term can be written in terms of the common difference and the first term, 𝑇 , as Recall that an arithmetic sequence is defined by a constant common difference, 𝑑, between any two consecutive terms. In this example, we want to determine the general term of a given arithmetic sequence.
Example 2: Finding the General Term of an Arithmetic Sequenceįind, in terms of 𝑛, the general term of the arithmetic sequence − 7, − 5, − 3, − 1, ….
0 kommentar(er)
