Find the (20)th term of the AP (55,52,49,46,\ldots).
Answer and explanation
Correct answer: \(-2\)
For this AP, the first term is \(a=55\) and the common difference is \(d=52-55=-3\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Thus, \(a_{20}=55+(20-1)(-3)=55-57=-2\). Hence, the correct answer is \(-2\). An answer such as \(-4\) may result from incorrectly using \(20d\); the correct multiplier is \(n-1=19\). Exam tip: in the nth-term formula of an AP, the common difference is added \((n-1)\) times.
Frequently asked questions
What is the correct answer to this question?
\(-2\)
Why is this the correct answer?
For this AP, the first term is \(a=55\) and the common difference is \(d=52-55=-3\). The \(n\)th term is given by \(a_n=a+(n-1)d\). Thus, \(a_{20}=55+(20-1)(-3)=55-57=-2\). Hence, the correct answer is \(-2\). An answer such as \(-4\) may result from incorrectly using \(20d\); the correct multiplier is \(n-1=19\). Exam tip: in the nth-term formula of an AP, the common difference is added \((n-1)\) times.
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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