If the (4)th term of an AP is (15) and the (12)th term is (55), what is the (16)th term?
Answer and explanation
Correct answer: 75
Given \(a_4=15\) and \(a_{12}=55\). Thus, \(a_{12}-a_4=8d\), so \(55-15=8d\) and \(d=5\). Now \(a_{16}=a_{12}+4d=55+4\times5=75\). Therefore, 75 is correct. The nearby option 80 would result from adding \(5d\) instead of the required \(4d\). Exam tip: use the difference between the term numbers to determine how many common differences are involved.
Frequently asked questions
What is the correct answer to this question?
75
Why is this the correct answer?
Given \(a_4=15\) and \(a_{12}=55\). Thus, \(a_{12}-a_4=8d\), so \(55-15=8d\) and \(d=5\). Now \(a_{16}=a_{12}+4d=55+4\times5=75\). Therefore, 75 is correct. The nearby option 80 would result from adding \(5d\) instead of the required \(4d\). Exam tip: use the difference between the term numbers to determine how many common differences are involved.
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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