What is the explicit rule for the geometric sequence?

Mathematics

2 answers:

makvit [3.9K]3 years ago

6 0

The answer is C. The formula for a geometric sequence is an = a1*r^n-1. If we plug in our numbers, we get an = 400*1/2^n-1. That is the same as C.

ANTONII [103]3 years ago

4 0

Answer:

an = 400*(1/2)^(n - 1) which is C is the most common answer.

Step-by-step explanation:

What did you have to do to get 400 as the first term?

There are two answers.

an = 400 * (1/2)^(n - 1)

an = 400 * (1/2)^n

Which one is the answer?

The answer is the one that leaves 400 as the first term.

a1 = 400*(1/2)^(n-1) should be the answer.

400*(1/2)^n is unfortunately sometimes used. In which case, the first term is a^0

A1 = 400 (1/2)^(n - 1) is the usual for that describes the series.

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Answer:

47.3 m³

Step-by-step explanation:

The garden shed is made up of a rectangular prism and a pyramid.

<h3><u>Volume of a rectangular prism</u></h3>

$\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}$

<h3><u>Volume of a pyramid</u></h3>

<u />

From inspection of the given diagram, the slant height of the pyramid is 3.5 m.

Calculate the perpendicular height of the pyramid using Pythagoras Theorem:

$\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}$

Therefore:

$\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}$

<h3><u>Volume of the garden shed</u></h3>

$\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}$