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What is the sum of the numbers in the series below? 15 11 7 . . . (–129)

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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

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.