The 12th term of an AP is -41 given that the first term is 3, find the 20th term.
To find the 20th term of an arithmetic progression (AP), we need to know the common difference (d) between consecutive terms.
The formula to find the nth term of an AP is given by:
tn = a + (n - 1) * d,
where tn is the nth term, a is the first term, n is the position of the term, and d is the common difference.
In this case, we have the 12th term (-41) and the first term (3). We need to find the common difference (d) in order to apply the formula.
Using the formula tn = a + (n - 1) * d,
-41 = 3 + (12 - 1) * d,
Simplifying:
-41 = 3 + 11 * d,
-44 = 11 * d,
d = -4.
Now that we have the common difference (d = -4), we can use the formula to find the 20th term.
tn = a + (n - 1) * d,
t20 = 3 + (20 - 1) * -4,
t20 = 3 + 19 * -4,
t20 = 3 + (-76),
t20 = -73.
Therefore, the 20th term of the AP is -73.
3 + 11d = -41
Now, knowing d, find
3+19d