Answer:
The sum of this series is 255
Step-by-step explanation:
First, we need to identify the equation for the arithmetic series, so it has the form
an = a1 + (n-1)d
Where an is the nth term, a1 is the first term and d is a common difference.
In this case, a1 = 3 and the common difference is 5 because
8 - 3 = 5
13 - 8 = 5
18 - 13 = 5
Then, the equation for the arithmetic series is
an = 3 + (n-1)5
Now, let's identify the position of the term 48, so replacing an = 48 and solving for n, we get:
48 = 3 + (n - 1)5
48 - 3 = (n - 1)5
45 = (n - 1)5
45/5 = n - 1
9 = n - 1
9 + 1 = n
10 = n
Therefore, 48 is the 10th term of the series.
Finally, the sum of the first n terms of an arithmetic series is equal to
Sn = n(a1 + an)/2
So, replacing n = 10, a1 = 3, and an = 48, we get that the sum of this series is
Sn = 10(3 + 48)/2
Sn = 10(51)/2
Sn = 510/2
Sn = 255
So, the answer is 255