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Since you're adding each number, n_next=99:

n_x=n_x-1+x | This is our basic formula

n_x=n_x-1+100 | We know that we're adding 100 to the current x, and the current x is equal to n_x-1+x, so the next x must be 100

n₁₀₀=n_100-1+100

n₁₀₀=n₉₉+100 | We subtract 1, giving us the previous x

First sequence begins with:0 to 9 =45 + 100 =145
n =9 - 0 + 1 =10 terms
Second sequence begins with:10 to 19          =145
n =19 - 10 + 1 =10 terms