In an AP, if the 7th and 13th terms are known, which of the following relations is always true for the 10th term?
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Answer and explanation
Correct answer: \(a_{10}=\frac{a_7+a_{13}}{2}\)
The indices 7, 10 and 13 are equally spaced by 3, so their AP terms are also equally spaced. Therefore, the middle term is the average: \(a_{10}=\frac{a_7+a_{13}}{2}\). Exam tip: look for equally spaced term numbers.
Frequently asked questions
What is the correct answer to this question?
\(a_{10}=\frac{a_7+a_{13}}{2}\)
Why is this the correct answer?
The indices 7, 10 and 13 are equally spaced by 3, so their AP terms are also equally spaced. Therefore, the middle term is the average: \(a_{10}=\frac{a_7+a_{13}}{2}\). Exam tip: look for equally spaced 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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