Question

Given the explicit rule, f(n) = 2n - 3, generate the first four terms in the sequence.

a) 1, 4, 7, 10
b) -1, 1, 5, 9
c) 2, 4, 6, 8
d) 3, 6, 9, 12

Answer 1

The first four terms of the sequence generated by the rule f(n) = 2n - 3 are -1, 1, 3, and 5, which correspond to option b in the provided choices.

Step-by-step explanation:

The student's question involves generating the first four terms of the sequence using the explicit rule f(n) = 2n - 3. To do this, we substitute the values of n into the rule for the first four terms (where n = 1, 2, 3, and 4 respectively).

• For n = 1: f(1) = 2(1) - 3 = 2 - 3 = -1

• For n = 2: f(2) = 2(2) - 3 = 4 - 3 = 1

• For n = 3: f(3) = 2(3) - 3 = 6 - 3 = 3

• For n = 4: f(4) = 2(4) - 3 = 8 - 3 = 5

Thus, the first four terms of the sequence are -1, 1, 3, and 5. This corresponds to option b in the multiple-choice list provided by the student.