given a geomatric progression 2,6,18,54... find the smallest value of n such that the nth term is greater than 100000

Mathematics

1 answer:

stiks02 [169]2 years ago

6 0

Answer:

hello,

Step-by-step explanation:

$u_1=2=2*3^0\\u_2=6=2*3^1\\u_3=18=2*3^2\\u_4=54=2*3^3\\\\....\\u_n=2*3^{n-1}\geq 100000\\\\3^{n-1}\geq 50000\\\\(n-1)*ln(3)\geq ln(50000)\\\\n-1\geq 9,848586...\\\\n\geq 10.848586....\\\\\boxed{n=11}\\$

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