MATH QSTION please help me?

Emma has been given a sum of money to invest in a part-time business. She is considering two options: A and B:





If Emma invests in a bussing selling fruit juice (A) she is told her return should be $2300 in the first year. Every following year her return can be estimated by adding $500 to the previous year’s return.





The first 3 terms are $2300, $2800, $3300.


A: Is the sequence of returns arithmetic, geometric or neither? Give a reason for answer.


B: Find her total return over 10 years by calculating the sum of the first 10 terms of the sequence.





If Emma invests in a business selling sports shoes her return the first year should be $6000. Every following year her return will be 80% of last years return.


A: is the sequence of returns arithmetic, geometric or neither. Give reason to answer.


B: Find her total return over 10 years by calculating the sum of the first 10 terms of the sequence.

MATH QSTION please help me?
A.it is arithmetic sequence as the difference is constant.


nth term=a+(n-1)d


a is 1st term=$2300


d is difference=$500


B.return=n/2[2a+(n-1)d]


=10/2[2*2300+9*500]


=5[4600+4500]


=5*9100


=$45500








the sequence will be geometric %26amp;denoted by


nth term=a(1+r)^(n-1)


a is 1st term ($6000)


r is rate of increase
Reply:In an arithmetic sequence, the terms follow this basic pattern:


{a, a+d, a +2d, a+3d, a + 4d,...)


d can be any number and is the same for all terms.





In a geometric sequence, the terms follow this basic pattern:


{a, a*r, a*r^2, a*r^3, a*r^4,...)


r can be any number and is the same for all terms.





So, for business a:


A: the sequence of returns looks like:


{2300, 2800, 3300, 3800, 4300, 4800,...}


= {2300, 2300+500, 2300 +2*500, 2300+3*500,...}


So, this is a ARITHMETIC sequence





B:The sum of the first 10 terms is:


2300 + 2800+ 3800 +...


=(10*2300) + (500+1000+1500 +2000+...)


=(10 *2300) + 500*(1+2+3+4+5+6+7+8+9)


=23000 +500*(45)


=45500


alternative: the well-known formula for summing up terms in a arithemtic sequence is:


=n*[2a+(n-1)*d]/2


note: this sequence assumes that n starts at 1


=10*[2*2300 + 9*500]/2


=45500








For business b:


A: the sequence of returns is


{6000, 6000*0.8, (6000*0.8)*0.8, (6000*0.8*0.8)*0.8),...}


={6000, 6000*0.8, 6000* 0.8^2, 6000* 0.8^3,...}


and so is a GEOMETRIC sequence





B:The total return can easiest be found using a well-known formula:


=a*[1-r^(n+1)]/(1-r)


note: this sequence assumes n starts at 0.


=6000*(1-0.8^10)/(1-0.8)


=26778.77








here's a few links on this:


http://en.wikipedia.org/wiki/Geometric_s...


http://en.wikipedia.org/wiki/Arithmetic_...



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