To determine which sequence follows the rule [tex]\(a_n = a_{n-1} + 7\)[/tex], let's examine each sequence step-by-step to ensure that each term is 7 more than the previous term.
Sequence A: [tex]\(11, 18, 25, 32, \ldots\)[/tex]
1. [tex]\(18 - 11 = 7\)[/tex]
2. [tex]\(25 - 18 = 7\)[/tex]
3. [tex]\(32 - 25 = 7\)[/tex]
Every term in this sequence is obtained by adding 7 to the previous term. Therefore, sequence A follows the rule.
Sequence B: [tex]\(17, 24, 30, 38, \ldots\)[/tex]
1. [tex]\(24 - 17 = 7\)[/tex]
2. [tex]\(30 - 24 = 6\)[/tex]
3. [tex]\(38 - 30 = 8\)[/tex]
Not all terms are obtained by adding 7 to the previous term. Sequence B does not follow the rule.
Sequence C: [tex]\(-9, -2, 4, 9, \ldots\)[/tex]
1. [tex]\(-2 - (-9) = -2 + 9 = 7\)[/tex]
2. [tex]\(4 - (-2) = 4 + 2 = 6\)[/tex]
3. [tex]\(9 - 4 = 5\)[/tex]
Not all terms are obtained by adding 7 to the previous term. Sequence C does not follow the rule.
Sequence D: [tex]\(-15, -7, 1, 8, \ldots\)[/tex]
1. [tex]\(-7 - (-15) = -7 + 15 = 8\)[/tex]
2. [tex]\(1 - (-7) = 1 + 7 = 8\)[/tex]
3. [tex]\(8 - 1 = 7\)[/tex]
Not all terms are obtained by adding 7 to the previous term. Sequence D does not follow the rule.
After examining all the sequences, we can conclude that the sequence that follows the rule [tex]\(a_n = a_{n-1} + 7\)[/tex] is sequence A.
Thus, the correct answer is:
Sequence A: [tex]\(11, 18, 25, 32, \ldots\)[/tex]
