Compare and contrast arithmetic and geometric sequences.

1 answer:

7 0

The difference is that the arithmetic sequence uses addition and geometric sequence uses multiplication. The same is that they both have a rule To find the next term

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Determine whether the sequence converges or diverges. If it converges, give the limit.

vaieri [72.5K]

Answer:

The given series converges and $\lim_{n \to \infty} a_n =0$

Step-by-step explanation:

Given is 108, -18, 3,...

It is an alternate series. An alternate series is convergent if:

1. The series is decreasing.

2. If the last term (n-th term) of series converges to 0.

<u>Since each next term is less than its preceding term, so it is decreasing.</u>

First term, a = 108

Second term = -18

Common ratio, r = -18/108 = -1/6

General term, aₙ = a*rⁿ = 108*(-1/6)ⁿ

<u>When n increases to infinity, the exponent term will decreases to zero, and last term (n-th term) will converge to 0 as well.</u>

Hence, the given series converges.

Now limit will be: $\lim_{n \to \infty} a_n$

$\lim_{n \to \infty} 108*(-1/6)^n \\= 108*(-1/6)^\infty \\= 108*(1/\infty) \\= 108*0 \\= 0$

Hence, $\lim_{n \to \infty} a_n =0$

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2 years ago

Please help final exam

Finger [1]

I think the answer here would be D. When it rains several inches, the water level of the lake increases, because the word Causation means: the relationship between cause and effect; causality. If it rains a lot, it will cause the lake to increase. ( if help on ur exam use Socratic and brainly!❤️) Hope you do well!!!

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3 years ago

Make a table of values and create a line of best fit

Anni [7]

<h2>Explanation:</h2><h2></h2>

Hello! remember you have to write complete questions in order to get good and exact answers. Here I'll explain this in a general way assuming the following table:

$\begin{array}{cc}x & y\\0 & 0\\1 & 2\\2 & 4\\3 & 6\\4 & 8\\5 & 10\end{array}$

As you can see, x increases in steps of 1 units. So let's check the difference in y:

$\bullet \ \text{From x=0 to x=1} \\ \\ \Delta y=2-0=2 \\ \\ \\ \bullet \ \text{From x=1 to x=2} \\ \\ \Delta y=4-2=2 \\ \\ \\ \bullet \ \text{From x=2 to x=3} \\ \\ \Delta y=6-4=2 \\ \\ \\ \bullet \ \text{From x=3 to x=4} \\ \\ \Delta y=8-6=2 \\ \\ \\ \bullet \ \text{From x=4 to x=5} \\ \\ \Delta y=10-8=2$

So we have a constant difference and we can conclude the table represents a line. Since the line passes through then y is directly proportional to x, so we can write:

$y=kx \\ \\ Where: \\ \\ k \ is \ constant \ of \ proportionality \ or \ the \ slope$