If (a_{10}=a+9d=59) and (a_{25}=a+24d=149), what is (a_{40})?
Answer and explanation
Correct answer: 239
Subtracting the given terms gives \(a_{25}-a_{10}=15d=149-59=90\). Hence, \(d=6\). Now \(a_{40}=a_{25}+15d=149+15\times6=239\). Therefore, the correct answer is 239. Choosing 245 would incorrectly use 16 common differences; there are only 15 differences from the 25th term to the 40th term. Exam tip: To find \(d\) quickly, subtract two known terms and divide by the difference in their term numbers.
Frequently asked questions
What is the correct answer to this question?
239
Why is this the correct answer?
Subtracting the given terms gives \(a_{25}-a_{10}=15d=149-59=90\). Hence, \(d=6\). Now \(a_{40}=a_{25}+15d=149+15\times6=239\). Therefore, the correct answer is 239. Choosing 245 would incorrectly use 16 common differences; there are only 15 differences from the 25th term to the 40th term. Exam tip: To find \(d\) quickly, subtract two known terms and divide by the difference in their term numbers.
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.
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