The sum of five terms of an arithmetic progression is 70. The product of the extreme terms is 132. Find the five terms. a. 8, 12, 16, 20, 24 b. 10, 12, 14, 16, 18 c. 4, 8, 12, 16, 20 d. 6, 10, 14, 18, 22

To solve this problem, we need to use the formulas for the sum of an arithmetic progression (AP) and the property of an AP where the product of the extreme terms is equal to the product of the middle term and the number of terms.

1. The sum of an AP is given by the formula: S = n/2 * (a + l) where n is the number of terms, a is the first term, and l is the last term. We know that the sum of the five terms is 70, so we can write the equation: 70 = 5/2 * (a + l).

2. The product of the extreme terms is given by the formula: a * l = m^2 * n where m is the middle term and n is the number of terms. We know that the product of the extreme terms is 132, so we can write the equation: 132 = m^2 * 5.

Now we can check each of the options:

a. 8, 12, 16, 20, 24: The sum is 80 (not 70) and the product of the extreme terms is 192 (not 132).

b. 10, 12, 14, 16, 18: The sum is 70 and the product of the extreme terms is 180 (not 132).

c. 4, 8, 12, 16, 20: The sum is 60 (not 70) and the product of the extreme terms is 80 (not 132).

d. 6, 10, 14, 18, 22: The sum is 70 and the product of the extreme terms is 132.

So, the correct answer is option d. 6, 10, 14, 18, 22.