Write the first six terms of each arithmetic sequence. a_n = a_n-1 -0.4, a₁ = 1.6

Verified step by step guidance

1. Identify the first term of the arithmetic sequence, which is given as \(a_1 = 1.6\).
2. Recognize that the common difference \(d\) is the amount subtracted each time, so \(d = -0.4\).
3. Use the recursive formula \(a_n = a_{n-1} + d\) to find each subsequent term by subtracting 0.4 from the previous term.
4. Calculate the second term: \(a_2 = a_1 - 0.4\).
5. Continue this process to find the third, fourth, fifth, and sixth terms by repeatedly subtracting 0.4 from the previous term.

Key Concepts

Arithmetic Sequence

An arithmetic sequence is a list of numbers where each term after the first is found by adding a constant difference to the previous term. This difference can be positive, negative, or zero, and it defines the pattern of the sequence.

Recursive Formula for Sequences

A recursive formula defines each term of a sequence using the previous term(s). In this problem, the formula an = an-1 - 0.4 means each term is 0.4 less than the term before it, starting from the initial term a₁.

Finding Terms of a Sequence

To find terms of a sequence using a recursive formula, start with the given first term and repeatedly apply the formula to find subsequent terms. For example, subtract 0.4 from each term to get the next, until the desired number of terms is found.