What will be the next term in the sequence (1,8,19,34,53,\ldots)?
Answer and explanation
Correct answer: 76
The consecutive differences are \(8-1=7\), \(19-8=11\), \(34-19=15\), and \(53-34=19\). These differences increase by \(4\) each time, so the next difference is \(23\). Therefore, the next term is \(53+23=76\). Choosing \(74\) would give a difference of \(21\), which does not follow the given difference pattern. Exam tip: For such sequences, first list the consecutive differences and check their pattern.
Frequently asked questions
What is the correct answer to this question?
76
Why is this the correct answer?
The consecutive differences are \(8-1=7\), \(19-8=11\), \(34-19=15\), and \(53-34=19\). These differences increase by \(4\) each time, so the next difference is \(23\). Therefore, the next term is \(53+23=76\). Choosing \(74\) would give a difference of \(21\), which does not follow the given difference pattern. Exam tip: For such sequences, first list the consecutive differences and check 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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