Question
Determine the sum of the arithmetic series 6+11+16+.....+91
Answers
GPT 3.5
In order to find the sum of an arithmetic series, we need to calculate the average of the first and last term, and then multiply that average by the number of terms in the series.
The first term in the series is 6 and the last term is 91. The common difference between the terms is 11 - 6 = 5.
To find the number of terms, we can use the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference
Solving for n, we have:
91 = 6 + (n - 1) * 5
91 - 6 = 5n - 5
85 = 5n
n = 85 / 5
n = 17
So there are 17 terms in the series. Now we can find the average:
average = (first term + last term) / 2
average = (6 + 91) / 2
average = 97 / 2
average = 48.5
Finally, we can find the sum of the arithmetic series using the formula:
sum = average * number of terms
sum = 48.5 * 17
sum = 824.5
Therefore, the sum of the arithmetic series 6 + 11 + 16 + ... + 91 is 824.5.
The first term in the series is 6 and the last term is 91. The common difference between the terms is 11 - 6 = 5.
To find the number of terms, we can use the formula for the nth term of an arithmetic sequence:
nth term = first term + (n - 1) * common difference
Solving for n, we have:
91 = 6 + (n - 1) * 5
91 - 6 = 5n - 5
85 = 5n
n = 85 / 5
n = 17
So there are 17 terms in the series. Now we can find the average:
average = (first term + last term) / 2
average = (6 + 91) / 2
average = 97 / 2
average = 48.5
Finally, we can find the sum of the arithmetic series using the formula:
sum = average * number of terms
sum = 48.5 * 17
sum = 824.5
Therefore, the sum of the arithmetic series 6 + 11 + 16 + ... + 91 is 824.5.