Find the sum of the series: 17 + 27 + 37+….+ 417
(417-17)/10 = 40
S41 = 41/2 (17+417) = 8897
To find the sum of an arithmetic series, we can use the formula Sn = (n/2)(2a + (n-1)d), where a is the first term, d is the common difference, and n is the number of terms.
In this series, the first term is 17 (a = 17) and the common difference is 10 (d = 10) since we are adding 10 to each term.
To find the number of terms (n), we can use the formula an = a + (n-1)d, where an is the last term in the series.
Given that an = 417, we can rearrange the formula to solve for n:
417 = 17 + (n-1)10
400 = (n-1)10
40 = n-1
n = 40 + 1
n = 41
Substituting the values a = 17, d = 10, and n = 41 into the sum formula:
Sn = (41/2)(2(17) + (41-1)10)
Sn = (41/2)(34 + 40(10))
Sn = (41/2)(34 + 400)
Sn = (41/2)(434)
Sn = 41(217)
Sn = 8897
Therefore, the sum of the series 17 + 27 + 37 + ... + 417 is 8897.
To find the sum of a series, we can use the formula for the sum of an arithmetic series:
S = (n/2)(a + l)
where S is the sum of the series, n is the number of terms, a is the first term, and l is the last term.
First, we need to determine the values of a, l, and n.
In this case, the first term is a = 17 and the last term is l = 417.
To find the number of terms, we can use the formula for the nth term of an arithmetic sequence:
l = a + (n-1)d
where d is the common difference between terms.
Given that the common difference is 10 (each term is obtained by adding 10 to the previous term), we can solve the equation:
417 = 17 + (n-1)10
400 = 10n - 10
410 = 10n
n = 41
Now that we have obtained the values of a = 17, l = 417, and n = 41, we can substitute them into the formula for the sum of an arithmetic series:
S = (n/2)(a + l)
S = (41/2)(17 + 417)
S = 20.5(434)
S = 8887
Therefore, the sum of the series 17 + 27 + 37 + ... + 417 is 8887.