If aₙ = 4n + 7, which term is equal to 75?
Answer and explanation
Correct answer: n = 17
The governing concept is an explicit or general rule: a formula gives the value of a sequence directly for any term number n. To find which term has value 75, set the formula equal to 75: 4n + 7 = 75. Subtracting 7 from both sides gives 4n = 68, and dividing by 4 gives n = 17. Therefore, the required term is the seventeenth term, so option C is correct. Options A, B, and D do not satisfy the equation; their substitution gives 67, 71, and 79 respectively, rather than 75.
Frequently asked questions
What is the correct answer to this question?
n = 17
Why is this the correct answer?
The governing concept is an explicit or general rule: a formula gives the value of a sequence directly for any term number n. To find which term has value 75, set the formula equal to 75: 4n + 7 = 75. Subtracting 7 from both sides gives 4n = 68, and dividing by 4 gives n = 17. Therefore, the required term is the seventeenth term, so option C is correct. Options A, B, and D do not satisfy the equation; their substitution gives 67, 71, and 79 respectively, rather than 75.
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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