The given series has six terms. What is the sum of the terms of the series?
10 + 25 + 40 + . . . + 85
a=10
d=15
S6 = 6/2 (2a+5d)
To find the sum of the terms of a series, we need to first determine the pattern of the series. In this case, the series is an arithmetic sequence because the difference between consecutive terms is constant. The common difference can be found by subtracting any term from the next term. Let's find the common difference:
Difference between the 2nd term and the 1st term
= 25 - 10
= 15
So, the common difference is 15. Now we know the pattern is as follows:
10, 10 + 15, 10 + 15 + 15, ...
To find the sum of the series, we can use the formula for the sum of an arithmetic series:
Sum = (n/2) * (first term + last term),
where n represents the number of terms in the series.
In this case, n = 6 (as given in the question).
The first term is 10.
The last term can be found by adding the common difference (15) to the fifth term (10 + 15 * 4).
Last term = 10 + 15 * 4 = 10 + 60 = 70
Now we can substitute these values into the formula:
Sum = (6/2) * (10 + 70)
= 3 * 80
= 240
Therefore, the sum of the terms of the series is 240.