It is known that the fine brushwork Q of equal ratio sequence is not equal to 1, and am, an and AP are equal ratio sequence. It is proved that m, N and P are equal difference sequence

It is known that the fine brushwork Q of equal ratio sequence is not equal to 1, and am, an and AP are equal ratio sequence. It is proved that m, N and P are equal difference sequence

Because am, an and AP form a series of equal proportion numbers, then the middle term of equal proportion consists of:
（an)^2=am*ap
(A1 * q ^ (n-1)) ^ 2 = A1 * q ^ (m-1) * A1 * q ^ (p-1)
Then cancel A1, (Q ^ (n-1)) ^ 2 = q ^ (m-1) * q ^ (p-1)
Because Q ≠ + - 1
SO 2 (n-1) = (m-1) + (p-1)
That is, 2n = m + P
It can be explained that m, N and P are equal difference sequence