Find the 12th term from the end of the AP: –2, –4, –6,..., –100

The given arithmetic progression (AP) is –2, –4, –6,..., –100.

Step 1: Find the common difference (d) The common difference (d) in an AP is the difference between any two consecutive terms. Here, d = –4 - (–2) = –2.

Step 2: Find the last term (l) The last term given in the AP is –100.

Step 3: Find the first term (a) The first term (a) in the AP is –2.

Step 4: Find the total number of terms (n) The formula to find the total number of terms in an AP is: n = [(l - a) / d] + 1 Substituting the given values, we get: n = [(–100 - (–2)) / –2] + 1 n = [–98 / –2] + 1 n = 49 + 1 n = 50

Step 5: Find the 12th term from the end The nth term from the end in an AP is given by the formula: l - (n - 1) * d Substituting the given values, we get: –100 - (12 - 1) * –2 = –100 - 22 = –78

So, the 12th term from the end of the given AP is –78.