tmua 2018 Q16

tmua · Uk · paper2 1 marks Arithmetic Sequences and Series Properties of AP Terms under Transformation

In this question, $x _ { 1 } , x _ { 2 } , x _ { 3 } , \ldots$ is an arithmetic progression, all of whose terms are integers.
Let $n$ be a positive integer. If the median of the first $n$ terms of the sequence is an integer, which of the following three statements must be true?
I The median of the first $n + 2$ terms is an integer.
II The median of the first $2 n$ terms is an integer.
III The median of $x _ { 2 } , x _ { 4 } , x _ { 6 } , \ldots , x _ { 2 n }$ is an integer.

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In this question, $x _ { 1 } , x _ { 2 } , x _ { 3 } , \ldots$ is an arithmetic progression, all of whose terms are integers.

Let $n$ be a positive integer. If the median of the first $n$ terms of the sequence is an integer, which of the following three statements must be true?

I The median of the first $n + 2$ terms is an integer.

II The median of the first $2 n$ terms is an integer.

III The median of $x _ { 2 } , x _ { 4 } , x _ { 6 } , \ldots , x _ { 2 n }$ is an integer.

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20