The 3rd term of an arithmetic progression is -9 and the 7th term is -29. Find the 10th term of the progression

Answer Details

An arithmetic progression is a sequence of numbers where each term is obtained by adding a fixed value to the previous term. Let's call this fixed value "d". Then, the nth term of an arithmetic progression can be expressed as: an = a1 + (n-1)d where "an" is the nth term, "a1" is the first term and "n" is the position of the term. In this problem, we are given the 3rd and 7th terms, which are -9 and -29 respectively. Using the formula above, we can write two equations: a3 = a1 + 2d = -9 a7 = a1 + 6d = -29 We can solve this system of equations to find "a1" and "d". First, we can subtract the first equation from the second equation: 4d = -20 This gives us d = -5. Substituting this value of "d" into the first equation, we get: a1 + 2(-5) = -9 a1 = 1 So the first term is 1, and the common difference is -5. Now we can use the formula to find the 10th term: a10 = a1 + 9d a10 = 1 + 9(-5) a10 = -44 Therefore, the 10th term of the arithmetic progression is -44. Option A is the correct answer.