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The common ratio of both the formulas is 3 and 2. The first formula is explicit and the second is the recursive formula.
<h3>What is the recursive rule?</h3>A rule is defined such that its definition includes itself.
1.
The given sequence is
-2, -6, -18, -54
Common ratio ;
r = -6 / -2 = 3
This given formula is the explicit formula.
2.
The given sequence is
4, 8, 16, 32
Common ratio ;
r = 8 / 4 = 2
This given formula is the recursive formula.
Learn more about the recursive rule and explicit rules here:
#SPJ1
Step 1:
Here we have -3 in subtraction on the left side, so when we take it to the right we apply opposite operation of subtraction that is addition.
Step 2:
Next we have 4 in multiplication on left side, so dividing right side by 4,
Step 3:
taking log on both sides
Step 4:
Dividing right side by 2,
x= ln (3.75) /2 = 0.66088
Answer : x = 0.66088..