Using Gauss's method, the sum of the numbers in the given series [ 15 11 7 . . . . ( –129 ) ] is -2664.
What is an arithmetic sequence?
An arithmetic sequence is simply a sequence of numbers in which the difference between the consecutive terms is constant.
From Gauss's method nth term is an arithmetic sequence is expressed as;
n = (( first term - last term )/d) + 1
d is the common difference between terms.
Given the series in the question;
15 11 7 . . . (–129)
d = 15 - 11 = 4
Next, we find n
n = (( first term - last term )/d) + 1
n = (( 15 - (-129))/4) + 1
n = ( 144/4 ) + 1
n = 36 + 1
n = 37
Now, using the common difference between terms the sun will be;
S = 15 + 11 + 7 . . . -125 -129
Also
S = -129 -125 . . . + 7 + 11 + 15
We add
2S = -114, 114, 114 . . . . n
Hence, the sum will be;
2S = ( -114 ) × n
2S = ( -114 ) × 37
2S = -5328
S = -5328 / 2
S = -2664
Therefore, using Gauss's method, the sum of the numbers in the series [ 15 11 7 . . . (–129) ] is -2664.
Learn more about arithmetic sequence here: 15412619
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