Question

The explicit formula of an arithmetic sequence is an = -12 + (n - 1)5. Write the recursive formula using the form and then write the first 4 terms of the sequence.

A) Recursive formula: a_n = a_n-1 + 5, Terms: -12, -7, -2, 3
B) Recursive formula: a_n = a_n-1 - 5, Terms: -12, -17, -22, -27
C) Recursive formula: a_n = a_n-1 + 12, Terms: -12, 0, 12, 24
D) Recursive formula: a_n = a_n-1 - 12, Terms: -12, -24, -36, -48

Answer 1

The recursive formula for the arithmetic sequence is an = an-1 + 5, and the first four terms of the sequence are -12, -7, -2, 3.

Step-by-step explanation:

The explicit formula for an arithmetic sequence is given as an = -12 + (n - 1)5. To write the recursive formula, we need to express an in terms of the previous term an-1. We start with the first term (when n=1): a1 = -12. Since the sequence is arithmetic, and the difference between consecutive terms is 5 (as indicated by the +(n-1)5 in the formula), the recursive formula can be written as an = an-1 + 5. To find the first four terms, we use the recursive formula as follows:

• First term: a1 = -12
• Second term: a2 = a1 + 5 = -12 + 5 = -7
• Third term: a3 = a2 + 5 = -7 + 5 = -2
• Fourth term: a4 = a3 + 5 = -2 + 5 = 3

Therefore, the correct recursive formula and the first 4 terms of the sequence are as follows:

Recursive formula: an = an-1 + 5,
Terms: -12, -7, -2, 3