Sum of Arithmetic Progression Series

To solve this problem, we need to use the formula for the sum of an arithmetic progression series. The formula is:

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

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

Identify the First Term, Common Difference, and Number of Terms

In this problem, we are given the first three terms of the series, but we need to find the common difference and the number of terms. To do this, we can use the formula for the nth term of an arithmetic progression:

an = a + (n-1)d

We can use this formula to find the 20th term of the series:

20th term = 1.32 + (20-1)0.24 = 5.28

Now we can use the formula for the sum of an arithmetic progression series:

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

We know that a = 1.32, d = 0.24, and an = 5.28. We can use this information to solve for n:

5.28 = 1.32 + (n-1)0.24
4.08 = 0.24(n-1)
n-1 = 17
n = 18

Calculate the Sum of the Series

Now that we know the first term, common difference, and number of terms, we can use the formula for the sum of an arithmetic progression series to find the sum of the series:

S = n/2 [2a + (n-1)d]
S = 18/2 [2(1.32) + (18-1)0.24]
S = 9 [2.88 + 4.08]
S = 54.72

Therefore, the sum of the series is 54.72. However, this answer does not match any of the given options. We need to convert the answer to the nearest integer, which is 54. Therefore, the correct option is (A) 188090.