The sum of the first and the 9th term of an arithmetic progression is 24. What is the sum of the first nine terms of the progression?Select one:a. 216b. 108c. 54d. None of the above options

To solve this problem, we need to use the formula for the sum of an arithmetic progression.

Step 1: We know that the sum of the first and the 9th term of an arithmetic progression is 24. In an arithmetic progression, the nth term is given by a + (n-1)d, where a is the first term and d is the common difference. Therefore, we can write this as a + a + 8d = 24. This simplifies to 2a + 8d = 24.

Step 2: We also know that the sum of the first n terms of an arithmetic progression is given by n/2 * (2a + (n-1)d). We want to find the sum of the first 9 terms, so we substitute n = 9 into this formula to get 9/2 * (2a + 8d).

Step 3: From step 1, we know that 2a + 8d = 24. We substitute this into the formula from step 2 to get 9/2 * 24 = 108.

Therefore, the sum of the first nine terms of the progression is 108, so the correct answer is (b) 108.