In an AP, (a_{15}=70) and (a_{25}=120). What is (a_1)?
Answer and explanation
Correct answer: 0
In an AP, the difference between two terms equals the corresponding number of common differences. Thus, \(a_{25}-a_{15}=10d\), so \(120-70=10d\) and \(d=5\). Now, using \(a_{15}=a_1+14d\), we get \(70=a_1+14\times5\), hence \(a_1=0\). Option 5 is the common difference, not the first term. Exam tip: In \(a_n=a_1+(n-1)d\), remember to use \(n-1\).
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
In an AP, the difference between two terms equals the corresponding number of common differences. Thus, \(a_{25}-a_{15}=10d\), so \(120-70=10d\) and \(d=5\). Now, using \(a_{15}=a_1+14d\), we get \(70=a_1+14\times5\), hence \(a_1=0\). Option 5 is the common difference, not the first term. Exam tip: In \(a_n=a_1+(n-1)d\), remember to use \(n-1\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
