Checking for Membership in an Arithmetic Progression

MathematicsArithmetic ProgressionsMedium

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30. Birnji agzasy we tapawudy: a) $a_1=5$ we $d=1,4$; b) $a_1=2,7$ we $d=0,5$; ç) $a_1=-3,6$ we $d=1,2$; d) $a_1=0,6$ we $d=-1,2$ bolsa, arifmetik progressiýada 38,6 sanyň agza bolup biljekdigini

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Step 1

Salam Nurana, geliň, şu arifmetik progressiýalaryň hersinde 38.6 sanynyň agza bolup biljekdigini bilelikde barlap göreliň.

Arifmetik progressiýa

$$a_n = a_1 + (n-1)d$$
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Step 2

Arifmetik progressiýanyň umumy agzasynyň formulasy a n deňdir a bir goşulan n minus bir köpeldilen d. 38.6 sanynyň agza bolmagy üçin n sanymyz natural san bolmalydyr.

Şert: n = \frac{a_n - a_1}{d} + 1 \text{ netijäniň natural san bolmagy gerek.}

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Step 3

Ilki bilen, a punktuny barlaýarys. a bir bäşe we d bir butyn dörde deň. Formula goýup hasaplalyň.

a) barlagy

$$n = \frac{38.6 - 5}{1.4} + 1$$
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Step 4

38.6-dan 5-i aýyrsak 33.6 galýar. Ony 1.4-e bölsek 24 çykýar.

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Step 5

25 natural san bolany üçin, 38.6 bu progressiýanyň 25-nji agzasy bolup bilýär.

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Step 6

Indi b punktuny barlaýarys. a bir 2.7 we d 0.5.

b) barlagy

$$n = \frac{38.6 - 2.7}{0.5} + 1$$
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Step 7

38.6-dan 2.7-ni aýyrsak 35.9 bolýar. Ony 0.5-e bölsek 71.8 çykýar.

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Step 8

72.8 natural san däl, şonuň üçin 38.6 bu progressiýada agza bolup bilmeýär.

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About This Question

Subject
Mathematics
Topic
Arithmetic Progressions
Difficulty
Medium
Question Type
Open Ended

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