Final answer:
The first term of the arithmetic progression is 4, and the sum of its 49 terms is 784, calculated using the standard formulas for the nth term and sum of an A.P.
Step-by-step explanation:
The problem involves finding the first term and the sum of an arithmetic progression (A.P.) where the last term (49th term) is given as 28, and the common difference is 1/2.
Step-by-Step Solution:
Using the formula for the nth term of an A.P., which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference, we can find the first term as follows:
a1 = an - (n - 1)d = 28 - (49 - 1)(1/2) = 28 - 24 = 4.
To find the sum of the A.P., we use the formula Sn = n/2(2a1 + (n - 1)d), where Sn is the sum of the first n terms. Substituting the values, we get: S49 = 49/2(2×4 + (49 - 1)(1/2))
= 24.5(8 + 24)
= 24.5×32
= 784.
Therefore, the first term of the A.P. is 4, and the sum of the 49 terms is 784.