SOLUTION: tim did 10 lunges on day 1 and continued this doing 4 more lunges on each day.on day 7th he took a breakand did nt do any day day.what is the equation for this? express it in the f

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Question 1167337: tim did 10 lunges on day 1 and continued this doing 4 more lunges on each day.on day 7th he took a breakand did nt do any day day.what is the equation for this? express it in the form y=ax(x+b)+c, where a,b and c are constants.x= no of days and y=no of lunges tim Did
Answer by ikleyn(52884) About Me  (Show Source):
You can put this solution on YOUR website!
Tim did 10 lunges on day 1 and continued this doing 4 more lunges on each day.
On day 7th he took a break and did not do any day.
What is the equation for this?
express it in the form y=ax(x+b)+c, where a, b and c are constants. x= no of days and y=no of lunges Tim Did
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

The numbers of lunges per day form arithmetic progression with the first term of  a%5B1%5D = 10
and the common difference of  d = 4.


Use the formula for the sum of first n terms of an arithmetic progression

    S%5Bn%5D = %28%282a%5B1%5D+%2B+%28n-1%29%2Ad%29%2An%29%2F2.    (1)


In your problem

    S%5Bn%5D = %28%2820+%2B+%28n-1%29%2A4%29%2An%29%2F2.


They want you use x instead of n and y instead of S%5Bn%5D.
OK.  Then the formula takes the form

    y = %28%2820+%2B+4%28x-1%29%29%2Ax%29%2F2 = 2(x-1)*x + 10x = 2x^2 - 2x + 10x = 2x^2 + 8x = 2x(x+4).


Thus, your final formula is

    y = 2x*(x+4),  1 <= x <= 6.    (2)


Comparing with the form  y = ax(x+b) + c,  you see for the coefficients 'a', 'b' and 'c'

    a = 2;  b = 4;  c = 0.         (3)


Below in the Table, calculations are compared using formulas (2), (3)  with direct calculations of the cumulative sum 


      T      A      B      L      E   


day   every   cumulative sum       cumulative sum
       day    computed directly    computed by formula (2)

 1     10         10                    10

 2     14         24                    24

 3     18         42                    42

 4     22         64                    64

 5     26         90                    90

 6     30        120                   120


ANSWER.  For the given sequence, the formula is  y = 2x*(x+4).

Solved.