Question

Given the first term and the common difference of an arithmetic sequence, create the recursive formula, and find the first 4 terms of the sequence.

a. Recursive formula: a_n = a_(n-1) + d; First 4 terms: a_1, a_2, a_3, a_4
b. Recursive formula: a_n = a_1 + d; First 4 terms: a_2, a_3, a_4, a_5
c. Recursive formula: a_n = a_(n+1) + d; First 4 terms: a_0, a_1, a_2, a_3
d. Recursive formula: a_n = a_(n-1) - d; First 4 terms: a_0, a_1, a_2, a_3

Answer 1

The recursive formula for an arithmetic sequence is a_n = a_(n-1) + d. The first 4 terms of the sequence can be found using this formula.

Step-by-step explanation:

For an arithmetic sequence with a common difference (d) and a first term (a_1), the recursive formula can be written as:

a_n = a_(n-1) + d

To find the first 4 terms of the sequence, we can use this formula:

1. a_1 = a_1
2. a_2 = a_1 + d
3. a_3 = a_2 + d
4. a_4 = a_3 + d

So, the first 4 terms are a_1, a_1 + d, a_1 + 2d, a_1 + 3d.