a. a=-3,U4=1/9:r=......
b. U3=8,U4=32:a=........ ...
c U2=250,U4=6.250:a=......
d. U2=12,U5=-324:r=......
e. k-2,k-6,2k+39,......:k=
2. a. a = -3, U₄ = 1/9
[tex]un = ar {}^{n - 1} \\ u4 = - 3.r {}^{4 - 1} \\ \frac{1}{9} = - 3.r {}^{3} [/tex]
1/9. -⅓ = r³
-1/27 = r³
[tex]r = \sqrt[3]{ - \frac{1}{27} } = - \frac{1}{3} [/tex]
b. U₃ = 8 ------> ar² = 8
U₄ = 32 -----> ar³ = 32
[tex] \frac{ar {}^{3} }{ar {}^{2} } = \frac{32}{8} \\ r = 4[/tex]
ar² = 8
a.4² = 8
16a = 8
a = 8/16 = ½
c. U₂ = 250 ------> ar = 250
U₄ = 6250 ------> ar³ = 6250
[tex] \frac{ar {}^{3} }{ar } = \frac{6250}{250} \\ r {}^{2} = 25 \\ r = \sqrt{25} = 5[/tex]
ar = 250
a.5 = 250
a = 250/5 = 50
d. U₂ = 12 --------> ar = 12
U₅ = -324 --------> ar⁴ = -324
[tex] \frac{ar {}^{4} }{ar} = \frac{ - 324}{12} \\ r {}^{3} = - 27 \\ r = \sqrt[3]{ - 27} = - 3[/tex]
e. k - 2, k - 6, 2k + 3
Geometri
Rasio = Rasio
[tex] \frac{u2}{u1} = \frac{u3}{u2} \\ \frac{k - 6}{k - 2} = \frac{2k + 3}{k - 6} [/tex]
( k - 6 ) ( k - 6 ) = ( 2k + 3 ) ( k - 2 )
k² - 12k + 36 = 2k² - k - 6
2k² - k² - k + 12k - 6 - 36 = 0
k² + 11k - 42 = 0
( k + 14 ) ( k - 3 ) = 0
k = -14, k = 3
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