Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?
2 answers:
<h2>Answer:</h2>
The sequence that could be partially defined by the given recursive formula is:
-10, -7.5 , -5 , -2.5 ,........
<h2>Step-by-step explanation:</h2>We are given a recursive formula as:
for n≥1
Hence, from the given options we will check the difference of which sequence is: 2.5
A)
2.5, 6.25, 15.625, 39.0625, …
6.25-2.5=3.75
15.625-6.25=9.375
As we could see that the common difference is not 2.5
Hence, option: A is incorrect.
B)
2.5, 5, 10, 20
5-2.5=2.5
10-5=5
20-10=10
As the common difference is not 2.5.
Hence, option: B is incorrect.
C)
–10, –7.5, –5, –2.5, …
-7.5-(-10)=-7.5+10=2.5
-5-(-7.5)=5+7.5=2.5
and -2.5-(-5)=-2.5+5=2.5
As the common difference is 2.5.
Hence, option: C is correct.
D)
-10, -25 , 6.25 , 156.25
-25-(-10)=-25+10= -15
As the common difference is not 2.5
Hence, option: D is incorrect.
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