The 12th term of an A.P is minus41 given that the first term is 3,find the 20th term
To find the 20th term of an arithmetic progression (A.P), we need to know the common difference between terms.
First, let's find the common difference (d) using the given information:
The 12th term (a12) of the A.P is -41, and the first term (a1) is 3.
The formula to calculate the n-th term of an A.P is:
an = a1 + (n-1)d
Substituting the values into the formula:
a12 = a1 + (12-1)d
-41 = 3 + 11d
To find d, we subtract 3 from both sides of the equation:
-41 - 3 = 11d
-44 = 11d
Now, we can solve for d by dividing both sides of the equation by 11:
d = -44/11
d = -4
We have found that the common difference (d) between the terms is -4.
Using the value of d, we can find the 20th term (a20) of the A.P:
a20 = a1 + (20-1)d
a20 = 3 + (19)(-4)
a20 = 3 - 76
a20 = -73
Therefore, the 20th term of the given arithmetic progression is -73.
11 differences between 3 and -41
the difference is ... (-41 - 3) / 11 = -4
19 differences from the 1st term to the 20th
the 20th term is ... 3 + (19 * -4) = ?