Lexi wants to create an arithmetic sequence. She wants the 4th term to be 40 & t(5)=80. Is it possible to create an arithmetic sequence to fit her information? If it is possible, write the equation. If not, explain why not.
sure ...
term(4) = a + 3d = 40
term(8) = a + 7d = 80
subtract them:
4d = 40
d = 10
back in a+3d = 40 to find a
.....
take over.
To determine if it is possible to create an arithmetic sequence with the given information, we can use the formula for the general term of an arithmetic sequence:
t(n) = a + (n - 1)d
Where:
t(n) is the nth term of the sequence,
a is the first term of the sequence, and
d is the common difference between terms.
From the given information, we know that t(4) = 40 and t(5) = 80. Plugging these values into the formula, we get:
t(4) = a + (4 - 1)d = 40 --> a + 3d = 40 (Equation 1)
t(5) = a + (5 - 1)d = 80 --> a + 4d = 80 (Equation 2)
To determine if it is possible to create an arithmetic sequence, we need to check if these two equations are consistent and have a common solution.
Subtracting Equation 1 from Equation 2, we get:
(a + 4d) - (a + 3d) = 80 - 40
d = 40
Substituting the value of d = 40 into Equation 1, we get:
a + 3(40) = 40
a + 120 = 40
a = -80
Therefore, the first term (a) is -80 and the common difference (d) is 40.
The equation for this arithmetic sequence is:
t(n) = -80 + (n - 1)40
So, it is possible to create an arithmetic sequence that fits Lexi's given information.