Chapter 7.8, Problem 54STP

To determine

Todetermine:The explicit formula for the geometrical sequence $15,3,0.6,0.12,\dots$ out of four given series.

Answer to Problem 54STP

Option A is the correct answer

Explanation of Solution

Given information:

The given geometric sequence is $15,3,0.6,0.12,\dots$ and one of the following is explicit formula for it.

A. $a_n=15\cdot {\left(0.2\right)}^{n-1}$

B. $a_1=0.12;a_n=5\cdot a^{n-1}$ C. $a_1=15;a_n=0.2\cdot a^{n-1}$

D. $a_1=0.2\cdot {15}^{n-1}$ .

Conceptused:

A geometric sequence is given by $a,ar,a{r}^2,a{r}^3,\dots a{r}^{n-1},\dots$ , where “ a ” isthe first term and r the common ratio. The nth term of the sequence is called the explicit formula given by $a_1=a;a_n=a{r}^{n-1}$

Calculations:

The given sequenceis $15,3,0.6,0.12,\dots$ , that may be written as

  $15,3,0.6,0.12,\dots ,a{r}^{n-1},\dots =15,\left(15\cdot 0.2\right),\left(15\cdot {0.2}^2\right),\left(15\cdot {0.2}^3\right),\dots ,\left(15\cdot {0.2}^{n-1}\right),\dots$

Thus, the nth term or the explicit formula of the sequence is $a{r}^{n-1}=\left(15\cdot {0.2}^{n-1}\right)$ .

Hence, option A is the correct answer.

Conclusion:

Option A is the correct answer