Jika 2p + q, 6p + q, 14p + q adalah tiga suku deret geometri yang berurutan maka rasio deretnya adal.... Question from @shintanawang

October 2018 2 655 Report

Jika 2p + q, 6p + q, 14p + q adalah tiga suku deret geometri yang berurutan maka rasio deretnya adalah

izharulhaq78 $\frac{6p+q}{2p+q}=\frac{14p+q}{6p+q}\\(6p+q)^2=(14p+q)(2p+q)\\36p^2+12pq+q^2=28p^2+14pq+2pq+q^2\\36p^2+12pq+q^2=28p^2+16pq+q^2\\36p^2+12pq=28p^2+16pq\\36p^2-4pq=28p^2\\8p^2-4pq=0\\4p(2p-q)=0\\\\4p=0\\p=0\\\\\text{ atau}\\\\2p-q=0\\2p=q\\p=\frac{q}{2}$

$\frac{6p+q}{2p+q}=\frac{14p+q}{6p+q}\\\frac{6(\frac{q}{2})+q}{2(\frac{q}{2})+q}=\frac{14(\frac{q}{2})+q}{6(\frac{q}{2})+q}\\\frac{3q+q}{q+q}=\frac{7q+q}{3q+q}\\\frac{4q}{2q}=\frac{8q}{4q}\\2=2(\text{terbukti})\\\\\boxed{\therefore r=2}$

4 votes Thanks 9

josephmanuel A(u3) = u2(u2)
(2p+q) (14p+q) = (6p+q)²
28p² + 2pq+14pq + q² = 36p²+6pq+6pq + q²
28p² + 16pq + q² = 36p²+12pq + q²
28p² - 36p² = -4pq

-8p² = -4pq
p = -4pq / -8p
p = 1/2q

Barisannya = 2p+q , 6p+q , 14p+Q
= 2(1/2q)+p , 6(1/2q) +q , 14(1/2q) + q
= 2p , 4p , 8p

rasio = 4p/2p = 2

2 votes Thanks 4

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