Question

The terms of the increasing arithmetic sequence are positive. The terms of the increasing geometric sequence are positive. The values of the first terms of both sequences are the same, and the values of the fourth terms of both sequences are the same. Which of the following statements describes the values of the second terms of the sequences?

a) They are equal.
b) The arithmetic sequence's second term is greater.
c) The geometric sequence's second term is greater.
d) Their relationship cannot be determined.

Answer 1

The values of the second terms of the increasing arithmetic and geometric sequences are equal.

Step-by-step explanation:

The statement that describes the values of the second terms of the sequences is: a) They are equal.

In an increasing arithmetic sequence, each term is obtained by adding a constant difference to the previous term. In an increasing geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. Since the values of the first terms are the same, and the values of the fourth terms are the same, it implies that the second terms of both sequences must also be equal.