If the (5)th term of an AP is (27) and the (14)th term is (90), what is the (20)th term?
Answer and explanation
Correct answer: 132
From the 5th term to the 14th term, there are 9 equal gaps. Therefore, the common difference is \(d=\frac{90-27}{14-5}=\frac{63}{9}=7\). The 20th term is 6 places after the 14th term, so \(a_{20}=90+6\times7=132\). The value 126 would result from moving only 5 places and would correspond to the 19th term. Exam tip: when moving between two AP terms, count the gaps as \(n-m\).
Frequently asked questions
What is the correct answer to this question?
132
Why is this the correct answer?
From the 5th term to the 14th term, there are 9 equal gaps. Therefore, the common difference is \(d=\frac{90-27}{14-5}=\frac{63}{9}=7\). The 20th term is 6 places after the 14th term, so \(a_{20}=90+6\times7=132\). The value 126 would result from moving only 5 places and would correspond to the 19th term. Exam tip: when moving between two AP terms, count the gaps as \(n-m\).
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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