Find the number of terms in each series, the first term, and the last term. Then evaluate the sum. ∑^3_(n=1)(17n-25)
To find the number of terms in the series ∑^3_(n=1)(17n-25), we can use the formula for arithmetic sequences:
Number of terms = (last term - first term) / common difference + 1
First, let's find the first term:
Substituting n = 1 into the expression 17n - 25:
First term = 17(1) - 25 = 17 - 25 = -8
Next, let's find the last term:
Substituting n = 3 into the expression 17n - 25:
Last term = 17(3) - 25 = 51 - 25 = 26
Now we can calculate the number of terms using the formula:
Number of terms = (last term - first term) / common difference + 1
Since the common difference is not provided in the given series, we can calculate it by subtracting the first term from the second term:
Common difference = (17(2) - 25) - (17(1) - 25)
= (34 - 25) - (-8)
= 9 + 8
= 17
Now, we can find the number of terms:
Number of terms = (last term - first term) / common difference + 1
= (26 - (-8)) / 17 + 1
= (34 / 17) + 1
= 2 + 1
= 3
Therefore, there are 3 terms in the series.
To evaluate the sum, we can use the formula for the sum of an arithmetic series:
Sum = (number of terms / 2) * (first term + last term)
Using the values we found, we have:
Sum = (3 / 2) * (-8 + 26)
= 1.5 * 18
= 27
Therefore, the sum of the series ∑^3_(n=1)(17n-25) is 27.