Final answer:
After calculating the common difference of the arithmetic progression as 2.9, the 4th term is found to be 10.7. Since only whole number options were provided, the closest correct answer is (d) 10.
Step-by-step explanation:
To find the 4th term of an arithmetic progression (A.P) with the first term being 2 and the sum of the 1st and 6th terms being 16 1/2, we need to find the common difference first. The n-th term of an A.P is given by the formula a_n = a_1 + (n - 1)d, where a_n is the n-th term, a_1 is the first term, and d is the common difference. Since the sum of the 1st and 6th terms equals 16 1/2, we have the equation: 2 + 2 + 5d = 16 1/2.
By solving the above equation for d, we calculate the common difference as 14 1/2 / 5, which simplifies to 2 9/10 or 2.9. Now we can easily find the 4th term by plugging values into the n-th term formula: a_4 = 2 + (4 - 1) * 2.9, which gives us 2 + 3 * 2.9 = 2 + 8.7 = 10.7. Therefore, the 4th term of the A.P is 10.7, but since we only have whole number options, the closest answer is (d) 10.