hrmoon2003 hrmoon2003
  • 26-12-2019
  • Mathematics
contestada

I NEED HELP QUICKLY!!! What is the sum of the first 140 positive multiples of 3?
A) 10,010
B) 29,820
C) 29,610
D) 29,470

Respuesta :

jimrgrant1 jimrgrant1
  • 26-12-2019

Answer:

C

Step-by-step explanation:

The multiples of 3 are

3, 6, 9, 12, 15, ...........

The terms form an arithmetic sequence with common difference of 3.

The sum to n terms 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 = 3 and d = 3, thus

[tex]S_{140}[/tex] = [tex]\frac{140}{2}[/tex] [ (2 × 3) + (139 × 3) ]

                            = 70(6 + 417) ] = 70 × 423 = 29610 → C

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