Respuesta :
Answer:
= -4539
Step-by-step explanation:
147 + 130 + 113 + 96 +
arithmetic, with
a = 147 and d 130 - 147 = -17
Sn = (n/2)(2a + d(n - 1))
S34 = (34/2)(2*147 - 17(34 - 1))
= 17(294 - 561)
The sum of the first 34 numbers in the series 147+130+113+96+... is -4539.
What is an arithmetic sequence?
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
[tex]a_n = a_1 + (n-1)d[/tex]
where d is the difference and a₁ is the first term of the sequence.
For the given series the first term of the series is 147. The common difference between any two consecutive numbers is,
Common difference = 130 - 147 = -17
Now, the sum of the first 34 numbers in the series below will be,
Sum of the first 34 numbers
[tex]= \dfrac{n}{2}[2a+(n-1)d]\\\\= \dfrac{34}{2}[2(147)+(34-1)(-17)]\\\\[/tex]
= 17(294-561)
= 17(-267)
= -4539
Learn more about Arithmetic Sequence:
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