Which number should be added to (S_{95}) to get (S_{105})?
Answer and explanation
Correct answer: 1005
If \(S_n\) denotes the sum of the first \(n\) natural numbers, the required number is \(S_{105}-S_{95}\). Thus, we must add \(96+97+\cdots+105\). There are 10 terms, with average \(\frac{96+105}{2}=100.5\), so their sum is \(10\times100.5=1005\). A distractor such as 1015 can result from incorrectly counting the terms or the last term. Exam tip: the difference of two partial sums leaves only the intervening terms.
Frequently asked questions
What is the correct answer to this question?
1005
Why is this the correct answer?
If \(S_n\) denotes the sum of the first \(n\) natural numbers, the required number is \(S_{105}-S_{95}\). Thus, we must add \(96+97+\cdots+105\). There are 10 terms, with average \(\frac{96+105}{2}=100.5\), so their sum is \(10\times100.5=1005\). A distractor such as 1015 can result from incorrectly counting the terms or the last term. Exam tip: the difference of two partial sums leaves only the intervening terms.
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.
