In a sequence given by Tn = a + b bn the 6th and 13th terms are 22 and 71 respectively. Find the values of a and b.
done when you posted this under a different name.
look at your other post.
To find the values of a and b, we need to use the given information about the 6th and 13th terms of the sequence. Here's how we can do it:
Step 1: Identify the pattern of the sequence
We have a sequence given by Tn = a + b * bn, where Tn represents the nth term of the sequence and bn represents the value of n in the sequence.
Let's write out the terms of the sequence using this formula:
T1 = a + b * b1
T2 = a + b * b2
T3 = a + b * b3
...
T6 = a + b * b6
T7 = a + b * b7
...
T13 = a + b * b13
Step 2: Use the given information to create equations
From the given information, we know that:
T6 = 22 and T13 = 71.
Using these values, we can substitute them into the equations for the 6th and 13th terms:
Equation 1: T6 = a + b * b6 = 22
Equation 2: T13 = a + b * b13 = 71
Step 3: Solve the equations
Now, we have two equations with two unknowns (a and b). We can solve these equations simultaneously to find the values of a and b.
From Equation 1, we can isolate a + b * b6:
a + b * b6 = 22
a = 22 - b * b6
Next, substitute this expression for a in Equation 2:
22 - b * b6 + b * b13 = 71
Simplify this equation:
-b * b6 + b * b13 = 49
Factor out b:
b * (b13 - b6) = 49
Now, we have a linear equation in terms of b. Let's solve for b:
b13 - b6 = 49 / b
Cross-multiply:
b * (b13 - b6) = 49
Expand:
b13 - b6 = 49 / b
Multiply both sides by b:
b^2 * (b13 - b6) = 49
Divide both sides by (b13 - b6):
b^2 = 49 / (b13 - b6)
Take the square root of both sides:
b = sqrt(49 / (b13 - b6))
Now, substitute this value of b back into Equation 1 to solve for a:
a = 22 - b * b6
a = 22 - (sqrt(49 / (b13 - b6))) * b6
These equations will give you the values of a and b in the sequence.