Question

Which of the following options correctly identifies the first term (a1) and the common difference (d) in Lillian's payment plan modeled as an arithmetic sequence?

A) a1 = initial payment, d = total amount
B) a1 = total amount, d = initial payment
C) a1 = first installment, d = subsequent installment
D) a1 = subsequent installment, d = first installment

Answer 1

The first term (a1) and common difference (d) in an arithmetic sequence modeling a payment plan are the first installment and the subsequent installment increase, respectively.

Step-by-step explanation:

To identify the first term (a1) and the common difference (d) in an arithmetic sequence that models Lillian's payment plan, we can refer to the standard form of an arithmetic sequence. The first term, often represented as a1, is the initial amount in the sequence, and the common difference, represented as d, is the fixed amount that each term in the sequence increases or decreases by from one term to the next.

For a payment plan modeled as an arithmetic sequence, the initial payment is typically the first term (a1), and the constant amount that each subsequent payment changes by is the common difference (d). Therefore, the option that correctly identifies the first term and the common difference is:

C) a1 = first installment, d = subsequent installment