In an AP, (a_{25}=a_{10}+180) and (a_{10}=70). What is (a_{65})?
Answer and explanation
Correct answer: 730
In an AP, the difference between two terms equals the difference of their positions multiplied by the common difference. Thus, \(a_{25}-a_{10}=15d=180\), so \(d=12\). Now, \(a_{65}=a_{10}+(65-10)d=70+55\times12=730\). Hence, 730 is correct. The close distractor 710 may result from incorrectly counting the difference in term positions instead of using \(65-10\). Exam tip: use \(a_m-a_n=(m-n)d\) when two terms are given; finding the first term is unnecessary.
Frequently asked questions
What is the correct answer to this question?
730
Why is this the correct answer?
In an AP, the difference between two terms equals the difference of their positions multiplied by the common difference. Thus, \(a_{25}-a_{10}=15d=180\), so \(d=12\). Now, \(a_{65}=a_{10}+(65-10)d=70+55\times12=730\). Hence, 730 is correct. The close distractor 710 may result from incorrectly counting the difference in term positions instead of using \(65-10\). Exam tip: use \(a_m-a_n=(m-n)d\) when two terms are given; finding the first term is unnecessary.
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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