What is the sum of the first 16 terms of the given series:

$$ 6, \frac{13}{2},7, \frac{15}{2}... $$

This series is comprised of two series.

6 , 7 , ...8 

$$\frac{13}{2} , \frac{15}{2},...$$

16 terms of the original series will have 8 terms from both the series .

So , for first series - Sum of 8 terms

8th term = 6 +7 = 13

Sum = $$\frac{n}{2}(a + l) = \frac{8}{2}(6 + 13) = 76$$

So , for second  series - Sum of 8 terms

8th term = $$\frac{13}{2} + 7 = \frac{27}{2}$$

Sum = $$\frac{n}{2}(a + l) = \frac{8}{2}(\frac{13}{2} + \frac{27}{2}) = 80$$

So , the answer would be option c)156.