D o I p l a y M i n e c r a f t o r, F o r t n i t e?

Mathematics

2 answers:

elena-14-01-66 [18.8K]3 years ago

6 0

M I n e c r a f t I t s b e t t e r

Viktor [21]3 years ago

3 0

Answer:

mine craft

Step-by-step explanation:

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The sequence$$1,2,1,2,2,1,2,2,2,1,2,2,2,2,1,2,2,2,2,2,1,2,\dots$$consists of $1$'s separated by blocks of $2$'s with $n$ $2$'s i

kicyunya [14]

Consider the lengths of consecutive 1-2 blocks.

block 1 - 1, 2 - length 2

block 2 - 1, 2, 2 - length 3

block 3 - 1, 2, 2, 2 - length 4

block 4 - 1, 2, 2, 2, 2 - length 5

and so on.

Recall the formula for the sum of consecutive positive integers,

$\displaystyle \sum_{i=1}^j i = 1 + 2 + 3 + \cdots + j = \frac{j(j+1)}2 \implies \sum_{i=2}^j = \frac{j(j+1) - 2}2$

Now,

$1234 = \dfrac{j(j+1)-2}2 \implies 2470 = j(j+1) \implies j\approx49.2016$

which means that the 1234th term in the sequence occurs somewhere about 1/5 of the way through the 49th 1-2 block.

In the first 48 blocks, the sequence contains 48 copies of 1 and 1 + 2 + 3 + ... + 47 copies of 2, hence they make up a total of

$\displaystyle \sum_{i=1}^48 1 + \sum_{i=1}^{48} i = 48+\frac{48(48+1)}2 = 1224$

numbers, and their sum is

$\displaystyle \sum_{i=1}^{48} 1 + \sum_{i=1}^{48} 2i = 48 + 48(48+1) = 48\times50 = 2400$

This leaves us with the contribution of the first 10 terms in the 49th block, which consist of one 1 and nine 2s with a sum of $1+9\times2=19$ .

So, the sum of the first 1234 terms in the sequence is 2419.

8 0

2 years ago

A sea horse riding travels an average of 0.01 miles per hour. At that rate , how fast can a sea horse travel in 2.4 hours?

kondaur [170]

As for this problem, it would be best to approach this with a ratio to ratio approach. This would then involve the equation with fractions which is the common conversion from ratios to easily solve the problems concerning these. The equation then would look somehow like this:

0.01 miles / 1 hour = x miles / 2.4 hours

The easiest way would be just to multiply the numerator, which is the miles, to 2.4. So when it is multiplied to the numerator, the equation then would turn to:

0.01 miles x 2.4 / 1 hour = x miles / 2.4 hours

0.024 miles would be the answer.

5 0

3 years ago

Read 2 more answers

Jenny bought gas for her car. Gas cost $3.45 per gallon. She bought 12.2 gallons for her car. What was the total cost of gas for

Greeley [361]

Answer:

Gas prices $3.45

Jenny purchase 12.2 gallons of gas for her car.

12.2 x $3.45 = 42.09

A= $42.09

3 0

3 years ago