If a_n = 6n^2 - 1, what is the value of a_4 + a_2?
Answer and explanation
Correct answer: 118
The governing concept is evaluating a formula at two different indices and then adding the resulting terms. First calculate a_4: a_4 = 6(4^2) - 1 = 6(16) - 1 = 96 - 1 = 95. Next calculate a_2: a_2 = 6(2^2) - 1 = 6(4) - 1 = 24 - 1 = 23. Therefore, a_4 + a_2 = 95 + 23 = 118. Option A is correct. A likely error is to omit the -1 twice or to add the indices before applying the formula; those mistakes can produce distractor values such as 120 or other nearby numbers. Each term must be evaluated separately because the expression asks for the sum of two sequence terms, not the value of the rule at n = 6.
Frequently asked questions
What is the correct answer to this question?
118
Why is this the correct answer?
The governing concept is evaluating a formula at two different indices and then adding the resulting terms. First calculate a_4: a_4 = 6(4^2) - 1 = 6(16) - 1 = 96 - 1 = 95. Next calculate a_2: a_2 = 6(2^2) - 1 = 6(4) - 1 = 24 - 1 = 23. Therefore, a_4 + a_2 = 95 + 23 = 118. Option A is correct. A likely error is to omit the -1 twice or to add the indices before applying the formula; those mistakes can produce distractor values such as 120 or other nearby numbers. Each term must be evaluated separately because the expression asks for the sum of two sequence terms, not the value of the rule at n = 6.
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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