Training World magazine suggests that beginner runners build their training by increasing the minutes that they run each day using the sequence {7, 17, 27, 37,…} until they have completed a marathon. Which of the following is the recursive definition of this arithmetic sequence? an=an−1+10; a1=7

an=an−1−10; a1=7

an=an−1+10; a1=0

an=an−1−10; a1=0

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

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44

step-by-step explanation:

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