If in an AP (a_6=6x-5), (a_{13}=13x-33), and (a_{20}=20x-61), what is (a_{27})?
Answer and explanation
Correct answer: \(27x-89\)
The term indices increase by 7 each time. \(a_{13}-a_6=(13x-33)-(6x-5)=7x-28\), and \(a_{20}-a_{13}=7x-28\). Therefore, the same difference is added from \(a_{20}\) to \(a_{27}\): \(a_{27}=20x-61+7x-28=27x-89\). Hence, option C is correct. Exam tip: For equally spaced terms of an AP, the differences between the terms are equal.
Frequently asked questions
What is the correct answer to this question?
\(27x-89\)
Why is this the correct answer?
The term indices increase by 7 each time. \(a_{13}-a_6=(13x-33)-(6x-5)=7x-28\), and \(a_{20}-a_{13}=7x-28\). Therefore, the same difference is added from \(a_{20}\) to \(a_{27}\): \(a_{27}=20x-61+7x-28=27x-89\). Hence, option C is correct. Exam tip: For equally spaced terms of an AP, the differences between the terms are equal.
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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