Determine the sum of the arithmetic series 6+11+16+.....+91
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.
To find the sum of an arithmetic series, we need to know the first term, the last term, and the common difference.
In our case, the first term is 6, the last term is 91, and the common difference is 11 - 6 = 5.
To find the number of terms in the series, we can use the formula:
n = (last term - first term) / common difference + 1
Plugging in the values, we get:
n = (91 - 6) / 5 + 1
n = 85 / 5 + 1
n = 17 + 1
n = 18
So, there are 18 terms in the series.
To find the sum of the series, we can use the formula:
Sum = (n/2) * (first term + last term)
Plugging in the values:
Sum = (18/2) * (6 + 91)
Sum = 9 * 97
Sum = 873
Therefore, the sum of the arithmetic series 6+11+16+.....+91 is 873.
To find the sum of an arithmetic series, you can use the formula:
Sn = (n/2)(a1 + an),
where Sn is the sum of the series, n is the number of terms, a1 is the first term, and an is the last term.
In this case, the first term (a1) is 6 and the last term (an) is 91. To find the number of terms (n), we need to determine the pattern and find the common difference (d).
By observing the pattern, we can see that each term is obtained by adding 5 to the previous term. This means that the common difference (d) is 5.
To find the number of terms (n), we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d,
where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.
Using the given values, we can substitute and solve for n:
91 = 6 + (n - 1)5.
Simplifying the equation, we have:
91 = 6 + 5n - 5.
Combining like terms, we get:
91 - 6 + 5 = 5n.
Simplifying further, we have:
90 = 5n.
Dividing both sides by 5, we find:
n = 18.
Now that we know the number of terms (n) is 18, we can substitute this value along with the other given values (a1 = 6 and an = 91) into the sum formula:
Sn = (n/2)(a1 + an).
Sn = (18/2)(6 + 91).
Sn = 9(97).
Sn = 873.
Therefore, the sum of the arithmetic series 6 + 11 + 16 +...+ 91 is 873.