If (a_n=n^2-6n+13), what is the smallest term value?
Answer and explanation
Correct answer: 4
The term can be written as
a_n=n^2-6n+13=(n-3)^2+4
. Since the minimum value of
(n-3)^2
is 0, attained at n=3, the smallest term value is 4. Option 3 is a common confusion because it is the value of n, not the value of the term. Exam tip: rewrite a quadratic in completed-square form to find its minimum quickly.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The term can be written as
a_n=n^2-6n+13=(n-3)^2+4
. Since the minimum value of
(n-3)^2
is 0, attained at n=3, the smallest term value is 4. Option 3 is a common confusion because it is the value of n, not the value of the term. Exam tip: rewrite a quadratic in completed-square form to find its minimum quickly.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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