Start at 92. Create a pattern that adds 13 to each stop after 5 numbers
1 answer:
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The given data is shown in the table below.
x: -5 -4 -3 -2 -1 0 1
f(x): 35 24 15 8 3 0 -1
A graph of the data is shown below.
Calculate rates of change, r.
Interval: [-5, -1]
r = (35 - 3)/(-5+1) = -8 (tile -8)
Interval: [-4, -1]:
r = (24 - 3)/(-4 + 1) = -7 (tile -7)
Interval: [-3, 1]:
r = (15 + 1)/(-3 - 1) = -4 (tile - 4)
Interval: [-2, 1]
r = (8 + 1)/(-2 - 1) = -3 (tile -3)
Answer:
Tile Interval
----- ----------
-3 [-2, 1]
-4 [-3, 1]
-7 [-4, -1]
-8 [-5, -1]
x: -5 -4 -3 -2 -1 0 1
f(x): 35 24 15 8 3 0 -1
A graph of the data is shown below.
Calculate rates of change, r.
Interval: [-5, -1]
r = (35 - 3)/(-5+1) = -8 (tile -8)
Interval: [-4, -1]:
r = (24 - 3)/(-4 + 1) = -7 (tile -7)
Interval: [-3, 1]:
r = (15 + 1)/(-3 - 1) = -4 (tile - 4)
Interval: [-2, 1]
r = (8 + 1)/(-2 - 1) = -3 (tile -3)
Answer:
Tile Interval
----- ----------
-3 [-2, 1]
-4 [-3, 1]
-7 [-4, -1]
-8 [-5, -1]
The number of terms in the given arithmetic sequence is n = 10. Using the given first, last term, and the common difference of the arithmetic sequence, the required value is calculated.
<h3>What is the nth term of an arithmetic sequence?</h3>The general form of the nth term of an arithmetic sequence is
an = a1 + (n - 1)d
Where,
a1 - first term
n - number of terms in the sequence
d - the common difference
<h3>Calculation:</h3>The given sequence is an arithmetic sequence.
First term a1 = = 3/2
Last term an = = 5/2
Common difference d = 1/9
From the general formula,
an = a1 + (n - 1)d
On substituting,
5/2 = 3/2 + (n - 1)1/9
⇒ (n - 1)1/9 = 5/2 - 3/2
⇒ (n - 1)1/9 = 1
⇒ n - 1 = 9
⇒ n = 9 + 1
∴ n = 10
Thus, there are 10 terms in the given arithmetic sequence.
learn more about the arithmetic sequence here:
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Disclaimer: The given question in the portal is incorrect. Here is the correct question.
Question: If the first and the last term of an arithmetic progression with a common difference are ,
and 1/9 respectively, how many terms has the sequence?