Evaluate the sum of the first 120 terms of the series whose nth term is equal to (4 n - 14)
You can make use of:
Sum from n = 0 to N of n = 1/2 N (N+1)
n.....1.....2.....3.....4.....5.....6
N....-10...-6....-2.....2.....6.....10
The 120th term derives from L = a + (n - 1)d where a = the first term, n = the number of terms and d = the common difference.
Then, the sum is S = n(a + L)/2.
To evaluate the sum of the first 120 terms of the series, we need to find the value of each term and add them up.
The formula for finding the nth term of the series is: (4n - 14).
To find the sum of the first 120 terms, 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.
In this case, the first term (a) is the value of the series when n = 1, and the last term (l) is the value of the series when n = 120.
a = (4 * 1 - 14) = -10
l = (4 * 120 - 14) = 466
Now, let's plug these values into the sum formula:
S = (120/2)(-10 + 466)
S = 60(456)
S = 27360
Therefore, the sum of the first 120 terms of the series is 27360.