5. the numbers are being multiplied by 4 each time, so the geometric sequence would be
an= 1/2(4) ^(n-1)
6. the numbers are being multiplied by 1/4 each time, so the geometric sequence would be
an= 32(1/4)^(n-1)
an in the formula is what ever term in the sequence.
32 or 1/2 is the a which is the first term in the sequence.
4 or 1/4 is the r in the sequence because it is the common ratio so what the equation was multiplied by to get the next term.
(n-1) is because when you are using this equation to solve for whatever term (an) you must subtract the first number in the sequence to get an accurate number
an you can input whatever number when trying to solve.
C 39.99 adding it all together
There are 98 terms.
98*(33+130)/2 = 7987
Answer:
7x⁴ + 5x³ + 7x² + 6x + 5
Step-by-step explanation:
The given expression is
(5x4 + 5x3 + 4x - 9) + (2x4 + 7x2 + 2x + 14)
The first step is to open the brackets by multiplying each term inside each bracket by the term outside each bracket. Since the term outside each bracket is 1, the expression becomes
5x⁴ + 5x³ + 4x - 9 + 2x⁴ + 7x² + 2x + 14
We would collect like terms by combining each term with the same exponent or raised to the same power. The term would be arranged in decreasing order of the exponents. It becomes
5x⁴ + 2x⁴ + 5x³ + 7x² + 4x + 2x - 9 + 14
7x⁴ + 5x³ + 7x² + 6x + 5
A nice riddle, mathematical riddle.
Assuming a turtle winning means the declared winner is the weaker one actually won over the stronger one. In this context, the turtle winner is the one who has a lesser number of favourable votes.
The given rules for the points are as follows:
1. Point for the first choice must be greater than or equal to that of the second choice.
2. All points must be positive whole numbers.
Let's suppose we have Henry against Tim.
Henry is favourite of the voters and is the leading candidate, according to popular polls.
Tim is an excellent manipulator, sly, and everybody knows this.
On polling day, the vote count came out as follows (in point counts)
Henry Tim
2 1
2 1
2 1
2 1
2 1
2 1
10 1 (Henry's own vote)
1 100 (Tim's own vote)
------------------
17 107 TOTAL POINTS
So Tim the turtle was declared winner of the race, and since everything was according to rule, even a recount of the votes did not change the results.
Be aware, voting by districts (instead of popular votes) also exhibits a similar problem.
