In which sequence are the first term and the common difference equal?
Answer and explanation
Correct answer: (6, 12, 18, 24, …)
The first term is the first number in each sequence, and the common difference is the change from one term to the next. In option A, the first term is 6, while 12 − 6 = 6, 18 − 12 = 6, and 24 − 18 = 6. Thus d = 6, equal to the first term. In option B, the difference is 4, not 6. In option C, the difference is 0, and in option D, the difference is −6. Therefore only option A satisfies a₁ = d = 6. The sequence in A is an increasing AP whose terms rise by exactly its initial value.
Frequently asked questions
What is the correct answer to this question?
(6, 12, 18, 24, …)
Why is this the correct answer?
The first term is the first number in each sequence, and the common difference is the change from one term to the next. In option A, the first term is 6, while 12 − 6 = 6, 18 − 12 = 6, and 24 − 18 = 6. Thus d = 6, equal to the first term. In option B, the difference is 4, not 6. In option C, the difference is 0, and in option D, the difference is −6. Therefore only option A satisfies a₁ = d = 6. The sequence in A is an increasing AP whose terms rise by exactly its initial value.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Introduction to APs and common difference..
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