Chapter 9.1, Problem 8E

To determine

To Find: The first four terms and the eighth term of a recursively defined sequence.

Answer to Problem 8E

The first $4$ terms and the $8^{th}$ term of the sequence are $10,11,12.1,13.31$ and $19.487171$ respectively.

Explanation of Solution

Given Information: $d_1=10$ and $d_n=1.1d_{n-1}$ for all $n\ge 2$

Method Used: Substitute a given term in the recursive relation to find its next term.

Calculation: Put $n=2$ in the recursive relation and substitute the given value of $d_1=10$ in it to write

  $d_2=1.1d_{2-1}=1.1d_1=1.1\times 10=11$

Similarly, get

  $d_3=1.1d_2=1.1\times 11=12.1$

  $d_4=1.1d_3=1.1\times 12.1=13.31$

  $d_5=1.1d_4=1.1\times 13.31=14.641$

  $d_6=1.1d_5=1.1\times 14.641=16.1051$

  $d_7=1.1d_6=1.1\times 16.1051=17.71561$

  $d_8=1.1d_7=1.1\times 17.71561=19.487171$

Therefore, the first $4$ terms and the $8^{th}$ term of the sequence are $10,11,12.1,13.31$ and $19.487171$ respectively.