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3 years ago

A geometric sequence is defined by a the recursive formula t1 = 243, tn + 1 = tn/3

Mathematics

1 answer:

spayn [35]3 years ago

3 0

Answer:

tn = 243·(1/3)^(n-1)

Step-by-step explanation:

The recursive formula tells you the first term (243) and the common ratio (1/3). You can put these numbers into the general formula for the n-th term of a geometric sequence:

an = a1·r^(n-1) . . . . . where a1 is the first term and r is the common ratio

You want the n-th term of your sequence to be called tn, so ...

tn = 243·(1/3)^(n-1)

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The mean of a list of test scores is 80. Adding an additional test score of 92 caused the mean to rise to 82. After this additio

miv72 [106K]

Answer:

Step-by-step explanation:

The mean of a list of test scores is 80

Adding an additional test score of 92 caused the mean to rise to 82

To find:

After this additional, how many total test are in the list ?

Solution:

Let the total number of test at first = $n$

And sum of total score = $S$

As we know, mean = $\frac{sum \ of \ total \ observation}{number\ of \ total\ observation}$

$80= \frac{S}{n} \\$

Multiplying both sides by $n$

$80n=S$

Now, as adding an additional test score of 92 caused the mean to rise to 82,

$S+92=82\times(n+1)\\80n +92 = 82n+82 \ (given \ S =80n)$

$80n-82n =82-92\\-2n=-10$

By dividing both sides by minus ( - )

$2n =10$

By dividing both sides by 2

$n =5$

Thus, total number of test at first = $n$ = 5

And, after this additional score added, total number of tests are $n+1=6$

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3 years ago

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Step-by-step explanation:

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Answer:

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