If a_n = 7n + 4, what is the value of a_6 + a_10?
Answer and explanation
Correct answer: 120
The governing concept is substitution into an explicit or general rule for a sequence. The rule is a_n = 7n + 4, so calculate each requested term separately. For n = 6, a_6 = 7(6) + 4 = 42 + 4 = 46. For n = 10, a_10 = 7(10) + 4 = 70 + 4 = 74. Adding them gives a_6 + a_10 = 46 + 74 = 120. Hence option C is correct. It is important not to substitute only one index or add the indices first without applying the constant correctly. The nearby alternatives reflect such arithmetic or substitution mistakes; direct evaluation of both terms confirms that 120 is the only correct value.
Frequently asked questions
What is the correct answer to this question?
120
Why is this the correct answer?
The governing concept is substitution into an explicit or general rule for a sequence. The rule is a_n = 7n + 4, so calculate each requested term separately. For n = 6, a_6 = 7(6) + 4 = 42 + 4 = 46. For n = 10, a_10 = 7(10) + 4 = 70 + 4 = 74. Adding them gives a_6 + a_10 = 46 + 74 = 120. Hence option C is correct. It is important not to substitute only one index or add the indices first without applying the constant correctly. The nearby alternatives reflect such arithmetic or substitution mistakes; direct evaluation of both terms confirms that 120 is the only correct value.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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