If (S_{m+2}-S_m=151), what is the value of (m)?
Answer and explanation
Correct answer: 74
Let S_m be the sum of the first m natural numbers. In S_{m+2}-S_m, only the next two numbers, (m+1) and (m+2), remain. Thus, S_{m+2}-S_m=(m+1)+(m+2)=2m+3. Hence 2m+3=151, so 2m=148 and m=74. If m were 73, the difference would be 149, not 151. Exam tip: In differences of such sums, cancel the common initial terms and add only the extra terms.
Frequently asked questions
What is the correct answer to this question?
74
Why is this the correct answer?
Let S_m be the sum of the first m natural numbers. In S_{m+2}-S_m, only the next two numbers, (m+1) and (m+2), remain. Thus, S_{m+2}-S_m=(m+1)+(m+2)=2m+3. Hence 2m+3=151, so 2m=148 and m=74. If m were 73, the difference would be 149, not 151. Exam tip: In differences of such sums, cancel the common initial terms and add only the extra 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.
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