Suppose you create a seven-digit identification number so that the seventh digit is the...

Suppose you create a seven-digit identification number so that the seventh digit is the check digit. The check digit is the remainder when a weighted sum of the first six digits is divided by 7. The weighted sum is formed by multiplying each of the first six digits by the digit’s position. Thus, the weighted sum For example, if the first six digits of an identification number are 208455, then the weighted sum is1(2) + 2(0) + 3(8) +4(4) + 5(5) + 6(5) = 2 + 0 + 24 + 16 + 25 + 30 = 97. When the weighted sum is divided by 7, the remainder is 6. The complete identification number is 2084556.

You made a mistake when recording an identification number. The number 0724311 was recorded rather than 7024311.

a. What type of error was made?

b. Will this error be detected? Why or why not?