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2 years ago

Hi, I need help with this math question. Can you pls help me?

Mathematics

2 answers:

frozen [14]2 years ago

3 0

The third term is 245 and the first term is 5 -> To get from the first term to the third term, we multiply it by 49.

Since in a geometric sequence, the difference between each term has to be a constant multiplier or a sequence of multipliers -> We can find the second number to be 5 x 7 = 35

So, this geometric sequence is 5 ; 35 ; 245 and so on.

-> The common ratio of this sequence is 7. (and sorry if the things above don't make sense)

podryga [215]2 years ago

3 0

Answer:

Step-by-step explanation:

Given:

First term = 5
Third term = 245

Let the second term be "x".

⇒ 5, x, 245...

Thus, the following equations:

5 × (something) = x
x × (something) = 245

To find the common ratio between the three terms, we need to find the value of "x". Simplify both the equations to obtain the values of (something). Then compare both the values.

⇒ [5 × (something)] = x

⇒ [5 × (something)]/5 = x/5

⇒ (something) = x/5

⇒ x × (something) = 245

⇒ [x × (something)]/x = 245/x

⇒ (something) = 245/x

Now, let's compare both the results of (something).

⇒ x/5 = 245/x

⇒ x² = 5 x 245

⇒ x² = 1225

⇒ x = √1225 = 35

Substitute the second term into the sequence.

⇒ 5, x, 245 = 5, 35, 245

Looking at the sequence formed, we can tell that 7 is being multiplied to each term. Thus, 7 is the common ratio.

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Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

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By the Central Limit Theorem, a normal distribution.

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