If (a_1=3) and (a_{n+1}=a_n+n^2), what will be (a_6)?
Answer and explanation
Correct answer: 58
The recurrence requires adding consecutive squares: \(a_2=3+1^2=4\), \(a_3=4+2^2=8\), \(a_4=8+3^2=17\), \(a_5=17+4^2=33\), and \(a_6=33+5^2=58\). Hence, 58 is correct. Option 56 is incorrect because the correct sum \(1^2+2^2+3^2+4^2+5^2=55\) must be added to 3. Exam tip: to find \(a_6\), add squares from \(1^2\) through \(5^2\).
Frequently asked questions
What is the correct answer to this question?
58
Why is this the correct answer?
The recurrence requires adding consecutive squares: \(a_2=3+1^2=4\), \(a_3=4+2^2=8\), \(a_4=8+3^2=17\), \(a_5=17+4^2=33\), and \(a_6=33+5^2=58\). Hence, 58 is correct. Option 56 is incorrect because the correct sum \(1^2+2^2+3^2+4^2+5^2=55\) must be added to 3. Exam tip: to find \(a_6\), add squares from \(1^2\) through \(5^2\).
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.
