Question

How do I solve this??

Answer 1

Answer:

Step-by-step explanation:

Formula

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

Givens

Sn = 60

a =  3

Solution

You want integer values for d and n

60 = (2*a + (n - 1)*d) * n/2           Multiply both sides by 2

120 = (2*3 + (n - 1)*d ) * n    

120 = (6 + n*d - d) * n

120 = 6n + n^2*d - d*n

This gives some really wild results. I will list all of them here. and then discuss them.

These are the ones that give results without any question and are correct.

n         d         tn

2         54         3  57

3          17         3    20   37

4           8         3    11   19   27

Here are some that are the gift of the equation

20         0           3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Now the equation says the following 3 are correct, but are they? Can you have a negative n? The equation says yes, but I doubt your instructor will.

-5         5          

-1         63

-2        22

You can bring these up if you are in a classroom. I wouldn't if you have to submit this to a computer which has absolutely no ability whatever to think about exceptions. Even the 20 0 is one I wouldn't use.