The first term of an arithmetic progression is (14) and the sum of the first (16) terms is (824). What is the common difference?
Answer and explanation
Correct answer: 5
The sum of the first n terms of an AP is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Here, \(824=\frac{16}{2}[2(14)+15d]=8(28+15d)\). Thus, \(28+15d=103\), so \(15d=75\) and \(d=5\). If 4 were used, the sum would be 704, not 824. Exam tip: substitute the given \(a\), \(n\), and \(S_n\) directly into the sum formula to find \(d\).
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The sum of the first n terms of an AP is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Here, \(824=\frac{16}{2}[2(14)+15d]=8(28+15d)\). Thus, \(28+15d=103\), so \(15d=75\) and \(d=5\). If 4 were used, the sum would be 704, not 824. Exam tip: substitute the given \(a\), \(n\), and \(S_n\) directly into the sum formula to find \(d\).
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.
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