In the sequence (7,10,13,16,\ldots), which term is (10)?
Answer and explanation
Correct answer: Second term
The position of a term is found by counting from the beginning of the sequence, starting with position 1. In the sequence \(7,10,13,16,\ldots\), the number 7 is written first, so it is the first term. The next number, 10, is therefore the second term. This directly gives option B.
The common difference is 3 because each term increases by 3, but finding the difference is not necessary for this particular question. If we use the formula for an arithmetic progression, \(a_n=a+(n-1)d\), then \(a=7\) and \(d=3\). For \(n=2\), \(a_2=7+(2-1)3=10\). This confirms that 10 is the second term, not the first, third, or fourth.
Frequently asked questions
What is the correct answer to this question?
Second term
Why is this the correct answer?
The position of a term is found by counting from the beginning of the sequence, starting with position 1. In the sequence \(7,10,13,16,\ldots\), the number 7 is written first, so it is the first term. The next number, 10, is therefore the second term. This directly gives option B.
The common difference is 3 because each term increases by 3, but finding the difference is not necessary for this particular question. If we use the formula for an arithmetic progression, \(a_n=a+(n-1)d\), then \(a=7\) and \(d=3\). For \(n=2\), \(a_2=7+(2-1)3=10\). This confirms that 10 is the second term, not the first, third, or fourth.
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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