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Ufumbuzi - Mfulululizo wa kijiometri

Uwiano wa kawaida ni:

r = 0.5061728395061729

r=0.5061728395061729

Jumla ya mfululizo huu ni:

s = 244

s=244

Muundo mkuu wa mfululizo huu ni:

a_{n} = 162 \cdot {0.5061728395061729}^{n - 1}

a_n=162*0.5061728395061729^(n-1)

Neno la n la mfululizo huu ni:

162, 82, 41.50617283950618, 21.009297363206834, 10.634335702363952, 5.382811898727433, 2.7246331833064787, 1.3791353150069832, 0.6980808384603249, 0.3533495602083126

162,82,41.50617283950618,21.009297363206834,10.634335702363952,5.382811898727433,2.7246331833064787,1.3791353150069832,0.6980808384603249,0.3533495602083126

Tazama hatua

Maelezo kwa hatua

1. Pata uwiano wa kawaida

Pata uwiano wa kawaida kwa kugawanya neno lolote la mlolongo kwa neno lililotangulia:

$a_{2} a_{1} = \frac{82}{162} = 0.5061728395061729$

Uwiano wa kawaida ( $r$ ) wa mlolongo ni thabiti na unasawa na sehemu ya maneno mawili yanayofuatana.
$r = 0.5061728395061729$

2. Pata jumla

5 ziada steps

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

Kupata jumla ya mfululizo, chomeka neno la kwanza: $a = 162$ , uwiano wa kawaida: $r = 0.5061728395061729$ , na idadi ya vipengele $n = 2$ katika fomula ya jumla ya mfululizo wa kijiometri:

$s_{2} = 162 * ((1 - {0.5061728395061729}^{2}) / (1 - 0.5061728395061729))$

$s_{2} = 162 * ((1 - 0.25621094345374185) / (1 - 0.5061728395061729))$

$s_{2} = 162 * (0.7437890565462582 / (1 - 0.5061728395061729))$

$s_{2} = 162 * (0.7437890565462582 / 0.49382716049382713)$

$s_{2} = 162 \cdot 1.5061728395061729$

$s_{2} = 244$

3. Pata muundo mkuu

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

Kupata muundo mkuu wa mfululizo, chomeka neno la kwanza: $a = 162$ na uwiano wa kawaida: $r = 0.5061728395061729$ katika fomula ya mfululizo wa kijiometri:

$a_{n} = 162 \cdot {0.5061728395061729}^{n - 1}$

4. Pata neno la n

Tumia fomu kuu kupata kipimo cha nth

$a_{1} = 162$

$a_{2} = a_{1} \cdot r^{n - 1} = 162 \cdot {0.5061728395061729}^{2 - 1} = 162 \cdot {0.5061728395061729}^{1} = 162 \cdot 0.5061728395061729 = 82$

$a_{3} = a_{1} \cdot r^{n - 1} = 162 \cdot {0.5061728395061729}^{3 - 1} = 162 \cdot {0.5061728395061729}^{2} = 162 \cdot 0.25621094345374185 = 41.50617283950618$

$a_{4} = a_{1} \cdot r^{n - 1} = 162 \cdot {0.5061728395061729}^{4 - 1} = 162 \cdot {0.5061728395061729}^{3} = 162 \cdot 0.129687020760536 = 21.009297363206834$

$a_{5} = a_{1} \cdot r^{n - 1} = 162 \cdot {0.5061728395061729}^{5 - 1} = 162 \cdot {0.5061728395061729}^{4} = 162 \cdot 0.0656440475454565 = 10.634335702363952$

$a_{6} = a_{1} \cdot r^{n - 1} = 162 \cdot {0.5061728395061729}^{6 - 1} = 162 \cdot {0.5061728395061729}^{5} = 162 \cdot 0.03322723394276193 = 5.382811898727433$

$a_{7} = a_{1} \cdot r^{n - 1} = 162 \cdot {0.5061728395061729}^{7 - 1} = 162 \cdot {0.5061728395061729}^{6} = 162 \cdot 0.016818723353743695 = 2.7246331833064787$

$a_{8} = a_{1} \cdot r^{n - 1} = 162 \cdot {0.5061728395061729}^{8 - 1} = 162 \cdot {0.5061728395061729}^{7} = 162 \cdot 0.00851318095683323 = 1.3791353150069832$

$a_{9} = a_{1} \cdot r^{n - 1} = 162 \cdot {0.5061728395061729}^{9 - 1} = 162 \cdot {0.5061728395061729}^{8} = 162 \cdot 0.004309140978150153 = 0.6980808384603249$

$a_{10} = a_{1} \cdot r^{n - 1} = 162 \cdot {0.5061728395061729}^{10 - 1} = 162 \cdot {0.5061728395061729}^{9} = 162 \cdot 0.0021811701247426703 = 0.3533495602083126$

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Kwa nini kujifunza hii

Mfululizo wa kijiometri hutumika kwa kawaida kuelezea dhana katika hisabati, fizikia, uhandisi, biolojia, uchumi, sayansi ya kompyuta, fedha, na zaidi, kufanya kuwa zana muhimu kuwa nayo katika vifaa vyetu. Moja ya matumizi ya kawaida ya safu za kijiometri, kwa mfano, ni kuhesabu riba iliyopatikana au isiyo kulipwa, shughuli inayohusishwa sana na fedha ambayo inaweza kumaanisha kupata au kupoteza pesa nyingi! Matumizi mengine ni pamoja na, lakini kwa hakika hayajazuiliwa, kuhesabu uwezekano, kupima radioactivity kwa muda, na kubuni majengo.

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Mfulululizo wa kijiometri