To find b1, we can use the formula for the nth term of an arithmetic sequence:
Bn = B1 + (n-1)d
Where:Bn = the nth termB1 = the first termd = the common differencen = the term number
Given:B3 = 16B6 = 2
Since B3 = 16, we know that:B3 = B1 + (3-1)d16 = B1 + 2d
And since B6 = 2, we know that:B6 = B1 + (6-1)d2 = B1 + 5d
Now we have a system of equations:16 = B1 + 2d2 = B1 + 5d
Subtracting the first equation from the second equation, we get:-14 = 3dd = -14 / 3d = -4.67
Now we plug this value of d back into the first equation to solve for B1:16 = B1 + 2(-4.67)16 = B1 - 9.34B1 = 16 + 9.34B1 = 25.34
Therefore, b1 ≈ 25.34.
To find b1, we can use the formula for the nth term of an arithmetic sequence:
Bn = B1 + (n-1)d
Where:
Bn = the nth term
B1 = the first term
d = the common difference
n = the term number
Given:
B3 = 16
B6 = 2
Since B3 = 16, we know that:
B3 = B1 + (3-1)d
16 = B1 + 2d
And since B6 = 2, we know that:
B6 = B1 + (6-1)d
2 = B1 + 5d
Now we have a system of equations:
16 = B1 + 2d
2 = B1 + 5d
Subtracting the first equation from the second equation, we get:
-14 = 3d
d = -14 / 3
d = -4.67
Now we plug this value of d back into the first equation to solve for B1:
16 = B1 + 2(-4.67)
16 = B1 - 9.34
B1 = 16 + 9.34
B1 = 25.34
Therefore, b1 ≈ 25.34.