Final answer:
Using the given information, we find the common difference of the AP series and then calculate the sum of the first 16 terms.
Step-by-step explanation:
Given that the 8th term of the AP series is 15 and the sum of the first 8 terms is 36, we can find the common difference between consecutive terms of the series using the formula:
an = a + (n - 1)d
where a is the first term, n is the term number, and d is the common difference. Substituting the values, we have:
15 = a + 7d
Solving this equation, we find that a = 15 - 7d.
Now, we can find the sum of the first 16 terms of the series using the formula:
Sn = (n/2)(2a + (n - 1)d)
Substituting the values, we have:
S16 = (16/2)(2a + 15d)
Since the sum of the first 8 terms is 36, we can substitute this into the equation:
36 = (8/2)(2a + 7d)
Simplifying, we get:
18 = 4a + 14d
Substituting a = 15 - 7d, we have:
18 = 4(15 - 7d) + 14d
Simplifying further, we get:
18 = 60 - 14d + 14d
Finally, we get:
18 = 60.