MathDB

20

Part of 2022 AMC 10

Problems(2)

Sequence Blocked

Source: 2022 AMC10A #20

11/11/2022
A four-term sequence is formed by adding each term of a four-term arithmetic sequence of positive integers to the corresponding term of a four-term geometric sequence of positive integers. The first three terms of the resulting four-term sequence are 57, 60, and 91. What is the fourth term of this sequence?
<spanclass=′latex−bold′>(A)</span>190<spanclass=′latex−bold′>(B)</span>194<spanclass=′latex−bold′>(C)</span>198<spanclass=′latex−bold′>(D)</span>202<spanclass=′latex−bold′>(E)</span>206<span class='latex-bold'>(A) </span>190\qquad<span class='latex-bold'>(B) </span>194\qquad<span class='latex-bold'>(C) </span>198\qquad<span class='latex-bold'>(D) </span>202\qquad<span class='latex-bold'>(E) </span>206
AMCAMC 102022 AMC 10a2022 AMCSequencesarithmetic sequencegeometric sequence
Cyclic Quad Spam

Source: 2022 AMC10B #20

11/17/2022
Let ABCDABCD be a rhombus with ∠ADC=46∘\angle{ADC} = 46^{\circ}. Let EE be the midpoint of CD‾\overline{CD}, and let FF be the point on BE‾\overline{BE} such that AF‾\overline{AF} is perpendicular to BE‾\overline{BE}. What is the degree measure of ∠BFC\angle{BFC}?
<spanclass=′latex−bold′>(A)</span> 110<spanclass=′latex−bold′>(B)</span> 111<spanclass=′latex−bold′>(C)</span> 112<spanclass=′latex−bold′>(D)</span> 113<spanclass=′latex−bold′>(E)</span> 114<span class='latex-bold'>(A)</span>\ 110 \qquad <span class='latex-bold'>(B)</span>\ 111 \qquad <span class='latex-bold'>(C)</span>\ 112 \qquad <span class='latex-bold'>(D)</span>\ 113 \qquad <span class='latex-bold'>(E)</span>\ 114
geometryrhombusAMCAMC 102022 AMC2022 AMC 10BSolvable without cyclic