Chapter 8.1, Problem 41E

a.

To determine

To Compute : The first five terms of the sequence.

Answer to Problem 41E

The first five terms of the sequence are : 1060, 1123.6, 1191, 1262.5 and 1338.2 .

Explanation of Solution

Given Information :

The n^thterm of a sequence is given by, $a_{\text{n}}\text{=1000(1}{\text{.06)}}^{\text{n}}$ .   .........(1)

Calculation:

Substituting n = 1 in equation (1) gives the first term as,

  $a_1\text{=1000(1}{\text{.06)}}^1=1060$

Substituting n = 2 in equation (1) gives the second term as,

  $a_2\text{=1000(1}{\text{.06)}}^2=1123.6$

Substituting n = 3 in equation (1) gives the third term as,

  $a_3\text{=1000(1}{\text{.06)}}^3=1191$

Substituting n = 4 in equation (1) gives the fourth term as,

  $a_4\text{=1000(1}{\text{.06)}}^4=1262.5$

Substituting n = 5 in equation (1) gives fifth term as,

  $a_5\text{=1000(1}{\text{.06)}}^5=1338.2$

Conclusion:

Thus,

The first five terms of the sequence are : 1060, 1123.6, 1191, 1262.5 and 1338.2 .

b.

To determine

To Find : If the sequence is convergent or divergent.

Answer to Problem 41E

Obtained sequence is a divergent sequence.

Explanation of Solution

Given Information :

For $a_{\text{n}}\text{=1000(1}{\text{.06)}}^{\text{n}}$ , the sequence obtained is, 1060, 1123.6, 1191, 1262.5 and 1338.2 . . .

For the sequence 1060, 1123.6, 1191, 1262.5 and 1338.2 . . . , the limit is $\infty$

Therefore, the sequence is divergent .

Conclusion :

Thus,

The sequence is a divergent sequence.