Solution:

Given: Series is 7/2, 7, 21/2, 14 and the number of terms is 17.

We can find the sum of the series by using the formula for the sum of n terms of an arithmetic progression.

Arithmetic Progression: A sequence of numbers where each term is obtained by adding a fixed number to the previous term.

The series given is an arithmetic progression as the difference between any two consecutive terms is constant.

Formula: The sum of n terms of an arithmetic progression is given by the formula:

S_n = n/2 [2a + (n-1)d]

Where S_n is the sum of n terms, a is the first term, d is the common difference, and n is the number of terms.

Calculation:

Here, a = 7/2, d = 7 - 7/2 = 7/2 and n = 17.

Substituting these values in the formula, we get:

S_17 = 17/2 [2(7/2) + (17-1)(7/2)]

S_17 = 17/2 [7 + 16(7/2)]

S_17 = 17/2 [7 + 56]

S_17 = 17/2 x 63

S_17 = 535.5

Therefore, the sum of the given series up to 17 terms is 535.5.

Conclusion:

The sum of the given series up to 17 terms is 535.5. We used the formula for the sum of n terms of an arithmetic progression to obtain the solution.