Respuesta :
The sequence partially defined by the recursive formula f(n+1) = f(n)+2.5, n≥1 is -10, -7.5, -5, -2.5, …
Given recursive formula is f(n+1) = f(n)+2.5, n ≥ 1.
So the first term of the sequence is f(1) since n ≥ 1.
Given options for the sequences are:
a. 2.5, 6.25, 15.625, 39.0625, …
b. 2.5, 5, 10, 20
c. -10, -7.5, -5, -2.5, …
d. -10, -25, 62.5, 156.25
We compare the first term of each sequence with the given recursive formula.
a. 2.5, 6.25, 15.625, 39.0625, …
In this sequence, the first term, f(1) = 2.5
Using recursive formula, f(2) = f(1) + 2.5 = 2.5 +2.5 = 5.
But the second term in the given sequence is 6.25. So the recursive formula does not match with this sequence.
b.2.5, 5, 10, 20
Here, f(1) = 2.5
By the recursive formula, f(2) = f(1) + 2.5 = 5
f(3) = f(2) + 2.5 = 5 +2.5 = 7.5, which does not match with the third term of the given sequence. So this sequence is not defined by the recursive formula.
c. -10, -7.5, -5, -2.5, …
Here, f(1) = -10
Using recursive formula, f(2) = f(1) + 2.5 = -10 + 2.5 = -7.5
f(3) = f(2) + 2.5 = -7.5 +2.5 = -5
f(4) = f(3) +2.5 = -5 +2.5 = -2.5
So far the recursive formula matches with the given sequence. So the sequence defined partially by the recursive formula, f(n+1) = f(n)+2.5, n ≥ 1 is -10, -7.5, -5, -2.5, …
d. -10, -25, 62.5, 156.25
Here the first term is, f(1) = -10.
But the sequence which matches with the recursive formula and starting with -10 is option c. So this sequence does not need to be verified.
The question is incomplete. Find out the complete question below:
Which sequence could be partially defined by the recursive formula f(n+1) = f(n)+2.5, n≥1 ?
a. 2.5, 6.25, 15.625, 39.0625, …
b. 2.5, 5, 10, 20
c. -10, -7.5, -5, -2.5, …
d. -10, -25, 62.5, 156.25
Learn more about sequences at https://brainly.com/question/1275192
#SPJ4
