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De common ratio is:

r = 0, 0006799796006119816

r=0,0006799796006119816

De Som van deze series is:

s = 100070

s=100070

De general form van deze series is:

a_{n} = 100003 \cdot 0, 0006799796006119816^{n - 1}

a_n=100003*0,0006799796006119816^(n-1)

De nth term van deze series is:

100003, 68, 0, 04623861284161475, 3, 1441313492893245 E - 05, 2, 1379451791613657 E - 08, 1, 453759109056457 E - 11, 9, 885265383622399 E - 15, 6, 721778807499006 E - 18, 4, 570672468925256 E - 21, 3, 1079640399479755 E - 24

100003,68,0,04623861284161475,3,1441313492893245E-05,2,1379451791613657E-08,1,453759109056457E-11,9,885265383622399E-15,6,721778807499006E-18,4,570672468925256E-21,3,1079640399479755E-24

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Stapsgewijze uitleg

1. Vind de common ratio

Vind de common ratio door dividing enige term in de sequence door de term die comes before het:

$a_{2} a_{1} = \frac{68}{100003} = 0, 0006799796006119816$

De common ratio ( $r$ ) van de sequence is constant en equals de quotient van two consecutive begrippen.
$r =_{} T O K 0_{}$

2. Vind de Som

5 extra stappen

$s_{n} = a * ((1 - r^{n}) / (1 - r))$

Naar vind de Som van de series, plug de first term: $a =_{} T O K 0_{}$ , de common ratio: $r =_{} T O K 1_{}$ , en de getal van elements $n =_{} T O K 2_{}$ in de meetkundige reeks Som formule:

$s_{2} = 100003 * ((1 - 0, 0006799796006119816^{2}) / (1 - 0, 0006799796006119816))$

$s_{2} = 100003 * ((1 - 4, 6237225724843006 E - 07) / (1 - 0, 0006799796006119816))$

$s_{2} = 100003 * (0, 9999995376277427 / (1 - 0, 0006799796006119816))$

$s_{2} = 100003 * (0, 9999995376277427 / 0, 999320020399388)$

$s_{2} = 100003 \cdot 1, 0006799796006118$

$s_{2} = 100070, 99999999999$

3. Vind de general form

$a_{n} = a \cdot r^{n - 1}$

Naar vind de general form van de series, plug de first term: $a =_{} T O K 0_{}$ en de common ratio: $r =_{} T O K 1_{}$ in de formule voor meetkundige reeks:

$a_{n} = 100003 \cdot 0, 0006799796006119816^{n - 1}$

4. Vind de nth term

Use de general form naar vind de nth term

$a_{1} = 100003$

$100003 \cdot 0, 0006799796006119816^{2 - 1} = 100003 \cdot 0, 0006799796006119816^{1} = 100003 \cdot 0, 0006799796006119816 = 68$

$100003 \cdot 0, 0006799796006119816^{3 - 1} = 100003 \cdot 0, 0006799796006119816^{2} = 100003 \cdot 4, 6237225724843006 E - 07 = 0, 04623861284161475$

$100003 \cdot 0, 0006799796006119816^{4 - 1} = 100003 \cdot 0, 0006799796006119816^{3} = 100003 \cdot 3, 144037028178479 E - 10 = 3, 1441313492893245 E - 05$

$100003 \cdot 0, 0006799796006119816^{5 - 1} = 100003 \cdot 0, 0006799796006119816^{4} = 100003 \cdot 2, 1378810427300838 E - 13 = 2, 1379451791613657 E - 08$

$100003 \cdot 0, 0006799796006119816^{6 - 1} = 100003 \cdot 0, 0006799796006119816^{5} = 100003 \cdot 1, 4537154975915293 E - 16 = 1, 453759109056457 E - 11$

$100003 \cdot 0, 0006799796006119816^{7 - 1} = 100003 \cdot 0, 0006799796006119816^{6} = 100003 \cdot 9, 884968834557362 E - 20 = 9, 885265383622399 E - 15$

$100003 \cdot 0, 0006799796006119816^{8 - 1} = 100003 \cdot 0, 0006799796006119816^{7} = 100003 \cdot 6, 7215771601842 E - 23 = 6, 721778807499006 E - 18$

$100003 \cdot 0, 0006799796006119816^{9 - 1} = 100003 \cdot 0, 0006799796006119816^{8} = 100003 \cdot 4, 57053535286467 E - 26 = 4, 570672468925256 E - 21$

$100003 \cdot 0, 0006799796006119816^{10 - 1} = 100003 \cdot 0, 0006799796006119816^{9} = 100003 \cdot 3, 107870803823861 E - 29 = 3, 1079640399479755 E - 24$

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Geometric sequences zijn commonly used naar explain concepts in mathematics, physics, engineering, biology, ecoNeemics, computer science, finance, en more, making them een very useful tool naar have in ons toolkits. One van de most common applications van geometric sequences, voor voorbeeld, is calculating earned of unpaid samengestelde rente, een activity most commonly associated met finance die could gemiddelde earning of losing een lot van money! Other applications include, but zijn certainly Neet limited naar, calculating kansrekening, measuring radioactivity over time, en designing buildings.

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