Here are the first five terms of an arithmetic sequence

Here are the first five terms of an arithmetic sequence. 7, 13, 19, 25, 31. Find an expression, in terms of n, for the nth term of this sequence.

The first five terms of an arithmetic sequence, which are 7, 13, 19, 25, and 31, form the basis for finding an expression for the nth term of the sequence. In an arithmetic sequence, each term is obtained by adding a constant value to the previous term. To find the expression for the nth term of this sequence, we need to determine the common difference, which is the constant value added to each term to obtain the next term.

To find the common difference, we can subtract the second term from the first term, the third term from the second term, and so on. By doing this, we can observe that the common difference between each consecutive term is 6. This means that in this arithmetic sequence, the common difference, represented by the letter d, is equal to 6.

With the common difference identified, we can now construct an expression for the nth term of the sequence. The general formula for an arithmetic sequence is given by Tn = a + (n-1)d, where Tn represents the nth term, a is the first term, n is the position of the term in the sequence, and d is the common difference. Substituting the values we have for this sequence, we get the expression Tn = 7 + (n-1)6, which simplifies to Tn = 6n + 1. This is the expression, in terms of n, for the nth term of the given arithmetic sequence.

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