Question

Which of the following is an arithmetic sequence where a1 = 14 and d = −3?

options:
a. 14, 11, 8, 5, . . .
b. 14, 17, 20, 23, . . .
c. 3, 17, 31, 45, . . .
d. −3, 11, 25, 39, . . .

Answer 1

The arithmetic sequence with a first term (a1) of 14 and a common difference (d) of -3 is option a: 14, 11, 8, 5, ...

Step-by-step explanation:

An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference, known as the common difference (d), to the previous term. Given that the first term of the sequence (a1) is 14 and the common difference (d) is -3, we can generate the sequence by subtracting 3 from each term to get to the next term. Starting with the first term 14:

1. 14 (a1)
2. 14 + (-3) = 11 (a2)
3. 11 + (-3) = 8 (a3)
4. 8 + (-3) = 5 (a4)

Thus, the sequence that matches these conditions is 14, 11, 8, 5, and so on.

The correct option is: a. 14, 11, 8, 5, ...