Use the formula to evaluate the series 3-9+27-81+...-a8

1 answer:

6 0

In the given series, we see that the first term is 3 and the common ratio between the succeeding terms is -3. To solve for the sum of the first 8 terms, we use the equation,

Sum = (a1)(1 – r^n) / (1 – r)

Substituting the known terms,

Sum = (3)(1 – (-3)^8)/(1 - -3) = -4920

<span>Thus, the answer is -4920.</span>

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To solve this question, we use the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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 $s = \frac{\sigma}{\sqrt{n}}$ .