Chapter 4.7, Problem 66PPE

To determine

To find : the first six terms in the sequence and meaning of the sixth term in context of the situation.

Answer to Problem 66PPE

Thus, first six terms of the sequence are 30,36,42,48,54 and 60 respectively.

The sixth terms of the sequence means that the bamboo is 60 in. tall the sixth week.

Explanation of Solution

Given information: A cane of bamboo is 30 in. tall the first week and grows 6 in. per week thereafter.

Calculation:

The height of the bamboo in first week is 30 in. and grows 6 in. per week thereafter, so the bamboo is 36 in. tall the second week , 42 in. tall in third week and so on. This form an arithmetic sequence with first term $A\left(1\right)=30$ and common difference $d=6$ respectively.

Now, the first six terms of the sequence are

  $\begin{array}{l}A\left(1\right)=30\\ A\left(2\right)=A\left(1\right)+d=30+6=36\\ A\left(3\right)=A\left(2\right)+d=36+6=42\\ A\left(4\right)=A\left(3\right)+d=42+6=48\\ A\left(5\right)=A\left(4\right)+d=48+6=54\\ A\left(6\right)=A\left(5\right)+d=54+6=60\end{array}$

Thus, first six terms of the sequence are 30,36,42,48,54and 60 respectively.

The sixth terms means that the bamboo is 60 in. tall the sixth week.