Question

The 8th term of an AP series is 15, and the sum of its first 8 terms is 36. Find the sum of the first 16 terms of this AP series.

a. 72
b. 108
c. 144
d. 180

Answer 1

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.