In an AP, (a_6=2) and (a_{18}=-70). What is (a_{30})?
Answer and explanation
Correct answer: -142
The common difference is \(d=\frac{a_{18}-a_6}{18-6}=\frac{-70-2}{12}=-6\). Now, \(a_{30}=a_{18}+(30-18)d=-70+12(-6)=-142\). Hence, the correct answer is \(-142\). Choosing \(-136\) would result from using an incorrect difference in term numbers. Exam tip: when two terms are given, always use the difference between their subscripts.
Frequently asked questions
What is the correct answer to this question?
-142
Why is this the correct answer?
The common difference is \(d=\frac{a_{18}-a_6}{18-6}=\frac{-70-2}{12}=-6\). Now, \(a_{30}=a_{18}+(30-18)d=-70+12(-6)=-142\). Hence, the correct answer is \(-142\). Choosing \(-136\) would result from using an incorrect difference in term numbers. Exam tip: when two terms are given, always use the difference between their subscripts.
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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