Understanding the Series
The series given is 3.6, 4.7, 5.8, ..., which is an arithmetic sequence. In this series:
- The first term (a) is 3.6.
- The common difference (d) can be calculated as:
- 4.7 - 3.6 = 1.1
- 5.8 - 4.7 = 1.1.
Thus, the common difference is 1.1.
Finding the nth Term
The nth term of an arithmetic series can be calculated using the formula:
- Tn = a + (n-1)d
For this series, the nth term becomes:
- Tn = 3.6 + (n-1) * 1.1.
Sum of the Series
The sum of the first n terms (S) of an arithmetic series can be calculated with:
- S = n/2 * (a + Tn).
To find S for (n-2) terms, we replace n with (n-2):
- S = (n-2)/2 * (3.6 + T(n-2)).
Calculating T(n-2)
Using the nth term formula:
- T(n-2) = 3.6 + ((n-2)-1) * 1.1
- T(n-2) = 3.6 + (n-3) * 1.1.
Now, substitute T(n-2) back into the sum formula:
- S = (n-2)/2 * (3.6 + (3.6 + (n-3) * 1.1)).
This gives the sum of the series up to (n-2) terms in a systematic manner, allowing you to compute it for any desired n.