The (6)th term of an arithmetic progression is (29) and the (19)th term is (94). What is the sum of the first (19) terms?
Answer and explanation
Correct answer: \(931\)
For an AP, \(a_6=a+5d=29\) and \(a_{19}=a+18d=94\). Subtracting gives \(13d=65\), so \(d=5\). Hence, \(a=29-5\times5=4\). Now, \(S_{19}=\frac{19}{2}[2a+18d]=\frac{19}{2}[8+90]=931\). Therefore, \(931\) is correct. A value such as \(950\) can result from using an incorrect first term or number of terms. Exam tip: find \(a\) and \(d\) from the given terms before applying the sum formula.
Frequently asked questions
What is the correct answer to this question?
\(931\)
Why is this the correct answer?
For an AP, \(a_6=a+5d=29\) and \(a_{19}=a+18d=94\). Subtracting gives \(13d=65\), so \(d=5\). Hence, \(a=29-5\times5=4\). Now, \(S_{19}=\frac{19}{2}[2a+18d]=\frac{19}{2}[8+90]=931\). Therefore, \(931\) is correct. A value such as \(950\) can result from using an incorrect first term or number of terms. Exam tip: find \(a\) and \(d\) from the given terms before applying the sum formula.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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