Sum of Series

The given series is 3 1/2, 7, 10 1/2, 14, ...

To find the sum of the series, we need to identify the pattern in the series. We can see that the series is an arithmetic sequence with a common difference of 3 1/2.

Using the formula for the sum of an arithmetic sequence, we can find the sum of the series:

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

where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.

(a) Using the formula, if we take a = 3 1/2, d = 3 1/2, and n = 17 (as given in the question), we get:

S = 17/2[2(3 1/2) + (17-1)(3 1/2)]
S = 17/2[7 + 16(3 1/2)]
S = 17/2[7 + 56]
S = 17/2(63)
S = 535.5

So, the sum of the series to 17 terms is 535.5, which is closest to option (a) 530.

(b) Option (b) 535 is not correct as it is not the closest answer to the calculated sum.

(c) Option (c) 535 15 is not correct as it does not make sense.

(d) Option (d) none of these is also not correct as option (a) is the closest answer to the calculated sum.

Therefore, the correct answer is (a) 530.

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