Question

What is the recursive formula for this geometric sequence?–2, –16, –128, –1024, ...

Answer 1

bn=-2*8^n-1

Step-by-step expla

Answer 2

`b_n=-2\cdot 8^(n-1)`

Explanation:

Denote first four terms of the geometrc sequence as

`b_1=-2,\\ \\b_2=-16,\\ \\b_3=-128,\\ \\b_4=-1024.`

Note that

`b_2=b_1\cdot q\Rightarrow -16=-2\cdot 8;\\ \\b_3=b_2\cdot q\Rightarrow -128=-16\cdot 8;\\ \\b_4=b_3\cdot q\Rightarrow -1024=-128\cdot 8.`

Then the common ratio is

`q=8.`

Therefore, the recursive formula for the geometric sequence is

`b_n=b_1\cdot q^(n-1)\Roghtarrow b_n=-2\cdot 8^(n-1).`