Sum of n-terms of series 2.5, 5.8, 8.11, ...

To find the sum of the n-terms of the given series, we need to identify the pattern in the series and then use the formula for the sum of an arithmetic series.

The given series is 2.5, 5.8, 8.11, ...

Identifying the pattern:
To identify the pattern, let's find the differences between consecutive terms:
5.8 - 2.5 = 3.3
8.11 - 5.8 = 2.31
...
From the differences, we can observe that they are not constant, but they form a series:
3.3, 2.31, ...

Expressing the terms in terms of the first term:
To find the common difference between the terms, let's subtract the first term from the second term:
5.8 - 2.5 = 3.3
Similarly, subtracting the second term from the third term:
8.11 - 5.8 = 2.31
...
From the above calculations, we can see that the terms are formed by adding the differences to the first term. So, the nth term of the series can be expressed as:
2.5 + (n-1)(3.3)

Using the formula for the sum of an arithmetic series:
The sum of n terms of an arithmetic series can be calculated using the formula:
Sn = (n/2)(2a + (n-1)d)

where Sn represents the sum of n terms, a represents the first term, and d represents the common difference.

Calculating the sum:
In the given series, the first term is 2.5 and the common difference is 3.3.
Substituting these values into the formula, we get:
Sn = (n/2)(2(2.5) + (n-1)(3.3))
= (n/2)(5 + 3.3n - 3.3)

Simplifying this expression, we have:
Sn = (n/2)(3.3n + 1.7)

Therefore, the sum of n terms of the given series is (n/2)(3.3n + 1.7).