If the sum of the first (t) natural numbers is (231), what is the value of (t+5)?
Answer and explanation
Correct answer: 26
The sum of the first \(t\) natural numbers is \(\frac{t(t+1)}{2}\). Thus, \(\frac{t(t+1)}{2}=231\), so \(t(t+1)=462\). Since \(21\times22=462\), \(t=21\). Therefore, \(t+5=21+5=26\). Option 25 would result from taking \(t=20\), but the sum from 1 to 20 is 210. Exam tip: When a sum is given, first find \(n\) using \(\frac{n(n+1)}{2}\), then evaluate the expression asked.
Frequently asked questions
What is the correct answer to this question?
26
Why is this the correct answer?
The sum of the first \(t\) natural numbers is \(\frac{t(t+1)}{2}\). Thus, \(\frac{t(t+1)}{2}=231\), so \(t(t+1)=462\). Since \(21\times22=462\), \(t=21\). Therefore, \(t+5=21+5=26\). Option 25 would result from taking \(t=20\), but the sum from 1 to 20 is 210. Exam tip: When a sum is given, first find \(n\) using \(\frac{n(n+1)}{2}\), then evaluate the expression asked.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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