It is known that A1 = 2 points (an, an + 1) are on the image of function f (x) = x2 + 2x, where n = 1,2,3... (1) it is proved that the sequence {LG (1 + an)} is an equal ratio sequence

It is known that A1 = 2 points (an, an + 1) are on the image of function f (x) = x2 + 2x, where n = 1,2,3... (1) it is proved that the sequence {LG (1 + an)} is an equal ratio sequence

The point (an, an + 1) is on the image of function f (x) = x2 + 2x, so an + 1 = (an) ^ 2 + 2An, that is, (an + 1) + 1 = [(an) + 1] ^ 2, so LG (1 + an) = 2lg [(an-1) + 1], so {LG (1 + an)} is an equal ratio number with the first term of Lg3 and the common ratio of 2. From 1), we know that {LG (1 + an)} is an equal ratio sequence, so LG (TN) = LG [(1 + A1) (1 + A2)