Chapter 6.7, Problem 36E

To determine

The first four terms of the sequence with the given description based on the recursive rule and an explicit rule for the sequence.

Answer to Problem 36E

  $a_n=16{\left(\frac{1}{2}\right)}^{n-1}$

Explanation of Solution

Given information:

The first term of the sequence is 16. Each term of the sequence is half the preceding term.

Formula used:

  $a_n=r.a_{n-1}$

Calculation:

The given sequence is geometric:

  $a_1=16\&r=\frac{1}{2}$

The first 4 terms are:

  $16,8,4,2$

The graph will be:

  

The recursive rule for a geometric sequence is:

  $a_n=r.a_{n-1}$

Therefore,

  $a_1=16,a_n=\frac{1}{2}{a}_{n-1}$

The explicit rule for a geometric sequence is:

  $a_n=a_1{r}^{n-1}$

Therefore,

  $a_n=16{\left(\frac{1}{2}\right)}^{n-1}$

Conclusion:

  $a_n=16{\left(\frac{1}{2}\right)}^{n-1}$