In the sequence (2,3,6,11,18,27,\ldots), the successive differences are (1,3,5,7,9,\ldots). What will be the next term?
Answer and explanation
Correct answer: 38
The successive differences are consecutive odd numbers: \(1,3,5,7,9\). Therefore, the next difference is \(11\). Hence, the next term is \(27+11=38\). The answer \(36\) would result from adding \(9\) again, but the differences continue as increasing odd numbers. Exam tip: write the consecutive differences first to identify a sequence pattern quickly.
Frequently asked questions
What is the correct answer to this question?
38
Why is this the correct answer?
The successive differences are consecutive odd numbers: \(1,3,5,7,9\). Therefore, the next difference is \(11\). Hence, the next term is \(27+11=38\). The answer \(36\) would result from adding \(9\) again, but the differences continue as increasing odd numbers. Exam tip: write the consecutive differences first to identify a sequence pattern quickly.
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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