If (a_n=\frac{n(n+1)}{2}+3), what will be (a_{10})?
Answer and explanation
Correct answer: (58)
Substitute n=10 into the formula. The first part is \(\frac{10(10+1)}{2}=\frac{10\times11}{2}=55\). This is the sum of the first ten natural numbers, or the tenth triangular number. The formula then adds the fixed constant 3, so \(a_{10}=55+3=58\).
Therefore option A is correct. The constant addition must be included after evaluating the fraction; stopping at 55 would give option B, but that is only the triangular-number part and not the complete term. No further sequence pattern is needed because the explicit formula directly gives the value. The supplied answer and explanation correctly calculate both the variable part and the constant part.
Frequently asked questions
What is the correct answer to this question?
(58)
Why is this the correct answer?
Substitute n=10 into the formula. The first part is \(\frac{10(10+1)}{2}=\frac{10\times11}{2}=55\). This is the sum of the first ten natural numbers, or the tenth triangular number. The formula then adds the fixed constant 3, so \(a_{10}=55+3=58\).
Therefore option A is correct. The constant addition must be included after evaluating the fraction; stopping at 55 would give option B, but that is only the triangular-number part and not the complete term. No further sequence pattern is needed because the explicit formula directly gives the value. The supplied answer and explanation correctly calculate both the variable part and the constant part.
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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