Question

1. how can an arithmetic sequence be written with a recursive or explicit equation?

2. how are the terms of an arithmetic sequence found from its formula?"

Answer 1

An arithmetic sequence can be represented by a recursive or explicit formula, with the former relating each term to its predecessor and the latter providing direct computation for any term using the first term and the common difference.

Step-by-step explanation:

An arithmetic sequence can be expressed using either a recursive or an explicit formula. A recursive equation defines each term of the sequence based on the preceding term. For example, if an arithmetic sequence starts with a number 'a' and has a common difference 'd', the recursive equation would be:

an = an-1 + d, where n > 1 and a1 = a.

The explicit equation defines the nth term of the sequence without the need for the previous term. It can be written as:

an = a + (n - 1)d

To find the terms of an arithmetic sequence from its formula, you use the explicit formula if you want to calculate the nth term directly, or you use the recursive formula if you are building each term sequentially from the first term.