Write the following Arithmetic Sequence using a Recursive Formula: an = -5 + 2(n – 1)

Given:

To find:

The arithmetic sequence using a Recursive Formula.

Solution:

We have,

        ...(i)

The explicit formula of an AP is

        ...(ii)

where, a₁ is first term and d is common difference.

From (i) and (ii), we get

Now, the recursive formula of an AP is

Putting d=2, we get

Therefore, the arithmetic sequence using a Recursive Formula is defined as , where n>2 and .

Final answer:

The arithmetic sequence given by the recursive formula is an = -5 + 2(n - 1). Each term in the sequence can be found by substituting the corresponding value of n into the formula.

Explanation:

An arithmetic sequence is a sequence of numbers in which the difference between two consecutive terms is constant. In this case, the recursive formula for the arithmetic sequence is given as an = -5 + 2(n - 1).

To find any term in the sequence, substitute the value of n into the formula. For example, to find the first term (a1), plug-in n = 1. The formula becomes a1 = -5 + 2(1 - 1) which simplifies to a1 = -5.

Similarly, to find the second term (a2), plug-in n = 2. The formula becomes a2 = -5 + 2(2 - 1) which simplifies to a2 = -3. Continuing this pattern, each term in the sequence can be found by substituting the corresponding value of n into the formula.

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