Consider the following sequences:
A : (4, 7, 10, 13, 16, 19, ...) ..+3
B : (3, 10, 17, 24, 31, 38, ...) ..+7
C : (8, 19, 30, 41, 52, 63, ...) ..+11
D : (1, 14, 27, 40, 53, 66, ...) ..+13
How to calculate for example "41" in which sequence ?
PS: I'm looking for a fast method, because this numbers get higher to thousands of digits.
These are four arithnmetic sequences whose nth term $T_n=A+D(n-1)$, where $A$ is the first term and $D$ is the common difference. Here 41 is the fourth term in the fourth sequence wit $A=8$ and $D=11$, so $41=8+3.11$