Given that the height of the been seed grass follows the sequence: 12, 23, 34, 45, . . .
Thus, the common difference of the growth of the seed is 23 - 12 = 11.
The rule describing an arithmetic sequence with a first term, a, and a common difference, d, is given by
U = a + (n - 1)d
Given that the first term if the sequence of growth of the seed is 12 and the common difference is 11. the rule is given by:
U = 12 + 11(n - 1) = 12 + 11n - 11 = 1 + 11n
i.e. the rule is U = 1 + 11n.
Part B:
The height of the seed in 15 days is diven by
U = 1 + 11(15) = 1 + 165 = 166 inches.