Find the value of A + B if the A is the first term and B is the common difference of the sequence whose 4th term is 3 and 20th term is 35
what is fractions?
A + 3B = 3
A + 19B = 35
16B = 32
B = 2
so, A = -3
A+B = -1
To find the value of A + B, we first need to find the values of A and B separately.
Let's start by finding the value of A, which is the first term of the sequence. We are given that the 4th term of the sequence is 3.
We can use the formula for the nth term of an arithmetic sequence, which is given by:
An = A + (n - 1)B
Substituting n = 4 and An = 3 into the formula, we get:
3 = A + (4 - 1)B
3 = A + 3B
This gives us the equation:
A = 3 - 3B
Next, let's find the value of B, which is the common difference of the sequence. We are given that the 20th term of the sequence is 35.
Using the same formula, we substitute n = 20 and An = 35:
35 = A + (20 - 1)B
35 = A + 19B
Now, substitute the value of A from the previous equation into this equation:
35 = (3 - 3B) + 19B
Simplifying the equation, we get:
35 = 3 - 3B + 19B
35 = 3 + 16B
Subtracting 3 from both sides, we get:
32 = 16B
Dividing both sides by 16, we find:
B = 2
Now that we have the value of B, we can substitute it back into the equation for A to find its value:
A = 3 - 3B
A = 3 - 3(2)
A = 3 - 6
A = -3
Finally, we can find the value of A + B:
A + B = -3 + 2
A + B = -1
Therefore, the value of A + B is -1.