Chapter 9.1, Problem 7E

To determine

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

Answer to Problem 7E

The first $4$ terms and the $8^{th}$ term of the sequence are $2,4,8,16$ and $256$ respectively.

Explanation of Solution

Given Information: $c_1=2$ and $c_n=2c_{n-1}$ 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 $c_1=2$ in it to write

  $c_2=2c_{2-1}=2c_1=2\times 2=4$

Similarly, get

  $c_3=2c_2=2\times 4=8$

  $c_4=2c_3=2\times 8=16$

  $c_5=2c_4=2\times 16=32$

  $c_6=2c_5=2\times 32=64$

  $c_7=2c_6=2\times 64=128$

  $c_8=2c_7=2\times 128=256$

Therefore, the first $4$ terms and the $8^{th}$ term of the sequence are $2,4,8,16$ and $256$ respectively.