Respuesta :

Answer:

D

Step-by-step explanation:

The sum to n terms of an arithmetic series is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 12, d = 4 and n = 30 , then

[tex]S_{30}[/tex] = [tex]\frac{30}{2}[/tex] [ (2 × 12) + (29 × 4) ]

     = 15(24 + 116)

     = 15 × 140

     = 2100 → D

rahulsharma789888

The sum of the arithmetic series given a₁ =12, d = 4, and n = 30 is 2100, therefore the correct answer is D.

What is the Sum of arithmetic series?

The sum of n terms of an arithmetic series can be easily found using a simple formula which says that, if we have an arithmetic series whose first term is a and the common difference is d, then the formula of the sum of n terms of the arithmetic series is as follows

Sn = n/2 [2a₁ + (n-1)d].

as given in the problem

a₁ =12, d = 4, and n = 30

Sn = 30/2 [2×12 + (30-1)×4]

    = 2100

The sum of the arithmetic series given a₁ =12, d = 4, and n = 30 is 2100.

Learn more about the arithmetic series from here

https://brainly.com/question/16415816

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