What is the value of (S_{78}-S_{52}+S_{26}) for sums of the first (52), first (78), and first (26) natural numbers?
Answer and explanation
Correct answer: 2054
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{78}=\frac{78\times79}{2}=3081\), \(S_{52}=\frac{52\times53}{2}=1378\), and \(S_{26}=\frac{26\times27}{2}=351\). Hence, \(S_{78}-S_{52}+S_{26}=3081-1378+351=2054\). Exam tip: evaluate each \(S_n\) separately, then apply the signs in the expression carefully.
Frequently asked questions
What is the correct answer to this question?
2054
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{78}=\frac{78\times79}{2}=3081\), \(S_{52}=\frac{52\times53}{2}=1378\), and \(S_{26}=\frac{26\times27}{2}=351\). Hence, \(S_{78}-S_{52}+S_{26}=3081-1378+351=2054\). Exam tip: evaluate each \(S_n\) separately, then apply the signs in the expression carefully.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
