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Mathematics I – foundations – test 4: Sequences: arithmetic and geometric

10 multiple-choice and short-answer problems (Mathematics I). The solutions are shown after checking.

1. For the sequence $a_n=\frac{1}{2n}$, what is $a_5$?

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2. For $a_n=(-1{)}^n\frac{1}{2^n}$, what is $a_3$?

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3. For $a_n=\frac{3n+2}{n}$, what is $a_2$?

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4. What is the common difference $d$ of $1,3,5,7,\dots$?

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5. Arithmetic sequence: $a_1=1$, $d=2$. What is $a_6$?

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6. A phone company earned 2000 € on 1 March and 125 € more on each following day. How much did it earn on 31 March?

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7. How much did the company earn in total from 1 to 31 March?

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8. What is the sum of the first 100 terms of the arithmetic sequence with $a_1=4$, $d=6$?

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9. What is the common ratio $q$ of $2,4,8,16,\dots$?

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10. Geometric sequence: $a_1=2$, $q=2$. What is $a_6$?

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