30 , 29 , 27, 24, 20 , ...

Let us try and determine the difference between terms.\

a2-a1 = 20 - 30 = -1

a3- a2= 27- 29 = -2

a4- a3= 24- 27 = -3

a5- a4= 20 - 24 = -4

....

We notice that we do...

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30 , 29 , 27, 24, 20 , ...

Let us try and determine the difference between terms.\

a2-a1 = 20 - 30 = -1

a3- a2= 27- 29 = -2

a4- a3= 24- 27 = -3

a5- a4= 20 - 24 = -4

....

We notice that we do not have a constant difference between terms, However, we found that there is a sequence withthe difference between the terms.

Then,

a1= 30

a2= a1 - 1 = a1- 1(0)/2

a3= a2- 2 = (a1-2) -1 = a1- 3 = a1- 3(2)/2

a4= a3-3 = (a1-3) - 3= a1- 6 = a1- 4(3)/2

a5= a4-4 = (a1-6) - 4= a1- 10 = a1- 5(4)/2

a6= a5- 5 = (a1-10) - 5 = a1- 15 = a1- 6(5)/2

......

an = a1 - n(n-1)/2