Question

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

Answer 1

Answer:

$b_n=-2\cdot 8^{n-1}$

Step-by-step 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

$b_n=b_1\cdot q^{n-1}\Roghtarrow b_n=-2\cdot 8^{n-1}.$