Question

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

A. -2,124
B. -2,109
C. -2,052
D. -1,995

Answer 1

Using Gauss's method
Total number of terms = [15-(-129)]/4+1=36+1=37
Add
S=15+11+7+....-125-129
S=-129-125-...+7+11+15
--------------------------------
2S=-114-114-114...(37 times)
=>
sum=S=(1/2)*(-114)*37=-2109


Using AP, T(n)=15+11+7+....-129
T(n)=19-4n  => T(1)=15, T(37)=-129
S(n)=(1/2)(37)(T(1)+T(37)=(1/2)37(15-129)=2109

Answer 2

The sum of the numbers in the provided series in which the first term is 15 is -1,995. Option D is correct.

What is arithmetic sequence?

Arithmetic sequence is the sequence in which the next term is obtained by adding or subtracting the previous term with the same number for the whole series.

The summation of arithmetic sequence is found out using the following formula.

$S=\dfrac{n}{2}(a+l)$

Here, (a) is the first term of the sequence, (l) is the last term and (n) is the number of terms in sequence.

The series given in the problem is,

$15 + 11 + 7 + . . . + (-129)$

Here, the first term a=15 and the difference between two terms d=4. The last term of the sequence is -129. Thus, the number terms n is,

$a_n=a+(n-1)d\\-129=15+(n-1)4\\n=\dfrac{-129-15}{4}+1\\n=35$

Put the values in the sum formula,

$S=\dfrac{35}{2}(15+(-129))\\S=\dfrac{35}{2}(15+(-129))\\S=-1995$

Thus, the sum of the numbers in the provided series in which the first term is 15 is -1,995. Option D is correct.

Learn more about the arithmetic sequence here;

https://brainly.com/question/6561461

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