If (a_5=24) and (d=8), what is the value of (a_{19})?
Answer and explanation
Correct answer: 136
To find a term from a known term of an AP, use \(a_n=a_m+(n-m)d\). Thus, \(a_{19}=a_5+(19-5)d=24+14\times8=24+112=136\). Hence, 136 is correct. Getting 144 would indicate that the difference between the term positions was taken incorrectly. Exam tip: the number of common differences between \(a_m\) and \(a_n\) is always \(n-m\).
Frequently asked questions
What is the correct answer to this question?
136
Why is this the correct answer?
To find a term from a known term of an AP, use \(a_n=a_m+(n-m)d\). Thus, \(a_{19}=a_5+(19-5)d=24+14\times8=24+112=136\). Hence, 136 is correct. Getting 144 would indicate that the difference between the term positions was taken incorrectly. Exam tip: the number of common differences between \(a_m\) and \(a_n\) is always \(n-m\).
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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