What will be the next term in the sequence (2,11,26,47,74,\ldots)?
Answer and explanation
Correct answer: 107
The differences between consecutive terms are \(11-2=9\), \(26-11=15\), \(47-26=21\), and \(74-47=27\). These differences increase by \(6\) each time, so the next difference is \(33\). Therefore, the next term is \(74+33=107\). Choosing \(105\) would give a difference of \(31\), which does not follow the pattern. Exam tip: For a sequence, first list consecutive differences and look for their pattern.
Frequently asked questions
What is the correct answer to this question?
107
Why is this the correct answer?
The differences between consecutive terms are \(11-2=9\), \(26-11=15\), \(47-26=21\), and \(74-47=27\). These differences increase by \(6\) each time, so the next difference is \(33\). Therefore, the next term is \(74+33=107\). Choosing \(105\) would give a difference of \(31\), which does not follow the pattern. Exam tip: For a sequence, first list consecutive differences and look for their pattern.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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