In the sequence (1,5,14,30,55,\ldots), the successive differences are (4,9,16,25,\ldots). What will be the next term?
Answer and explanation
Correct answer: 91
The successive differences \(4,9,16,25\) are \(2^2,3^2,4^2,5^2\). Hence, the next difference is \(6^2=36\). Therefore, the next term is \(55+36=91\). Taking a difference such as \(30\) after \(25\) would be incorrect because the differences follow consecutive perfect squares. Exam tip: when a sequence pattern is unclear, list its successive differences first.
Frequently asked questions
What is the correct answer to this question?
91
Why is this the correct answer?
The successive differences \(4,9,16,25\) are \(2^2,3^2,4^2,5^2\). Hence, the next difference is \(6^2=36\). Therefore, the next term is \(55+36=91\). Taking a difference such as \(30\) after \(25\) would be incorrect because the differences follow consecutive perfect squares. Exam tip: when a sequence pattern is unclear, list its successive differences first.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
