Mathematics: What is the sum of the series? 4+12+36+108++8748 can someone first explain the log part? when you get your log result, do you round it?

What is the sum of the series? 4+12+36+108++8748 - id4123610887481199933, sebastianartiloufym8

Ответ:

carsengilbert

14.03.2022

$t_n = a r^{n-1}$

a = 4, r = 3, t_n = 8748

No rounding needed? It's a whole number

$8748 = 4 \cdot 3^{n-1} \\
\\ \displaystyle\frac{8748}{4} = 3^{n-1} \\ \\ 
2187 = 3^{n-1} \\ \\
\log_3(2187) = n - 1 \implies n = \log_3(2187) + 1 \implies \\ \\ \\
n = \frac{\ln 2187}{\ln 3} + 1 = 7 + 1 = 8$

$\displaystyle S_n=\frac{a(1-r^n)}{1-r} \implies S_8 =\displaystyle \frac{4(1 - 3^8)}{1 - 3} \\ \\ \\
= 13120$

Sum is 13120

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Ответ:

theatergeek005

29.08.2020

Mathematics

If c & c is 8 then to a and c it’s six if the scale factor is 5

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What is the sum of the series? 4+12+36+108++8748 can someone first explain the log part? when you get your log result, do you round it?

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