Question

A grass seed has grown to 12 millimeters tall. tomarow it will be 23 mm tall the next dy it will be 34 mm tall and on the next day it will be 45 mm tall write a rule to represent the height of the bean plant as an arithmetic sequence how tall will it be in 15 days

Answer 1

so hmm notice, 12, 23, 34, 45

is simply adding 11 units to get the next value, thus, our "common difference" is 11 then, and our first number is 12

$\bf n^{th}\textit{ term of an arithmetic sequence}\\\\ a_n=a_1+(n-1)d\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ d=\textit{common difference}\\ ----------\\ d=11\\ a_1=12 \end{cases}\\\\\\ a_n=12+(n-1)11\\\\ -------------------------------\\\\ \textit{on the 15th day n = 15}\qquad a_{15}=12+(15-1)11$