In an AP, (a_2+a_6=50) and (a_{10}=57). What is (a_{22})?
Answer and explanation
Correct answer: 121
Let the first term be \(a\) and the common difference be \(d\). Then \(a_2+a_6=(a+d)+(a+5d)=2a+6d=50\), so \(a+3d=25\). Also, \(a_{10}=a+9d=57\). Subtracting the two equations gives \(6d=32\), hence \(d=\frac{16}{3}\). Now \(a_{22}=(a+3d)+18d=25+18\times\frac{16}{3}=121\). Therefore, 121 is correct. A value such as 105 can result from using an incorrect common difference. Exam tip: subtract equations involving AP terms first to find \(d\) quickly.
Frequently asked questions
What is the correct answer to this question?
121
Why is this the correct answer?
Let the first term be \(a\) and the common difference be \(d\). Then \(a_2+a_6=(a+d)+(a+5d)=2a+6d=50\), so \(a+3d=25\). Also, \(a_{10}=a+9d=57\). Subtracting the two equations gives \(6d=32\), hence \(d=\frac{16}{3}\). Now \(a_{22}=(a+3d)+18d=25+18\times\frac{16}{3}=121\). Therefore, 121 is correct. A value such as 105 can result from using an incorrect common difference. Exam tip: subtract equations involving AP terms first to find \(d\) quickly.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
