Final answer:
The 12th term from the last of the given Arithmetic Progression (AP) is -26, found using the AP nth term formula and calculating the total number of terms.
Step-by-step explanation:
The Arithmetic Progression (AP) in question appears to begin with 10 and has subsequent terms 7, 4, and so on, ending with -62.
The common difference (d) is found by subtracting a term from the term that comes before it, which in this case is
-3 (7 - 10 = -3).
To find the 12th term from the last term, we will need to use the AP nth term formula:
- nth term of AP = a + (n-1)d, where a is the first term and d is the common difference.
Since -62 is the last term, let's consider it as Tn where n is the total number of terms.
To find the 12th term from the end, we want to find Tn-11, because the last term is Tn, the second to last is Tn-1, and so on.
First, we find n by rearranging the nth term formula to get:
n = [(Tn - a) / d] + 1.
Plugging in our values gives us
n = [(-62 - 10) / -3] + 1, which simplifies to n = 24.
Now we can find the 12th term from the last, which is the (24 - 11)th term or T13.
Using the nth term formula, T13 = 10 + (13 - 1)(-3), which simplifies to
T13 = 10 - 36 = -26.
Therefore, the 12th term from the last term of the given AP is -26.