MathDB

7

Part of 2015 AMC 10

Problems(2)

Sequence

Source: 2015 10A #7

2/4/2015
How many terms are there in the arithmetic sequence 13,16,19,…,70,7313, 16, 19, \dots, 70,73?
<spanclass=′latex−bold′>(A)</span>20<spanclass=′latex−bold′>(B)</span>21<spanclass=′latex−bold′>(C)</span>24<spanclass=′latex−bold′>(D)</span>60<spanclass=′latex−bold′>(E)</span>61 <span class='latex-bold'>(A) </span>20\qquad<span class='latex-bold'>(B) </span>21\qquad<span class='latex-bold'>(C) </span>24\qquad<span class='latex-bold'>(D) </span>60\qquad<span class='latex-bold'>(E) </span>61
LaTeXarithmetic sequenceAMC
Minus the Reciprocal of Function

Source: 2015 amc 10b #7

2/26/2015
Consider the operation "minus the reciprocal of," defined by a⋄b=a−1ba\diamond b=a-\frac{1}{b}. What is ((1⋄2)⋄3)−(1⋄(2⋄3))((1\diamond2)\diamond3)-(1\diamond(2\diamond3))? <spanclass=′latex−bold′>(A)</span>−730<spanclass=′latex−bold′>(B)</span>−16<spanclass=′latex−bold′>(C)</span>0<spanclass=′latex−bold′>(D)</span>16<spanclass=′latex−bold′>(E)</span>730<span class='latex-bold'>(A) </span> -\dfrac{7}{30} \qquad<span class='latex-bold'>(B) </span> -\dfrac{1}{6} \qquad<span class='latex-bold'>(C) </span> 0 \qquad<span class='latex-bold'>(D) </span> \dfrac{1}{6} \qquad<span class='latex-bold'>(E) </span> \dfrac{7}{30}
functionAMC