0 reads0 ratings0 helpful
If an arithmetic progression has first term \(a\), common difference \(d\), and \(n\) terms, which formula correctly represents the sum of its first \(n\) terms?
Advertisement
Answer and explanation
Correct answer: \(S_n=\frac{n}{2}[2a+(n-1)d]\)
The sum is \(S_n=\frac{n}{2}[2a+(n-1)d]\), since the last term is \(a+(n-1)d\). Option B gives only the \(n\)th term, not the sum. Exam tip: always check the \((n-1)d\) factor.
Frequently asked questions
What is the correct answer to this question?
\(S_n=\frac{n}{2}[2a+(n-1)d]\)
Why is this the correct answer?
The sum is \(S_n=\frac{n}{2}[2a+(n-1)d]\), since the last term is \(a+(n-1)d\). Option B gives only the \(n\)th term, not the sum. Exam tip: always check the \((n-1)d\) factor.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
Student feedback
Was this question useful?
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Difficulty
Easy0%
Medium0%
Hard0%
Was the explanation clear?
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
Advertisement