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What is the sum of the first 50 natural numbers?

PLEASE HELP ASAP CORRECT ANSWER ONLY PLEASE What is the sum of the first 50 natural numbers class=

Respuesta :

Answer:

1275

Step-by-step explanation:

The natural numbers 1, 2, 3, 4, ...... , 49, 50

The terms of natural numbers are the terms of an arithmetic sequence.

The sum to n terms of an arithmetic sequence is

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

where a is the first term and d the common difference

here a = 1, d = 1 and n = 50, hence

[tex]S_{50}[/tex] = [tex]\frac{50}{2}[/tex][ 2 + (49 × 1) ]

                           = 25(2 + 49) = 25 × 51 = 1275


tramserran

Answer:   1275

Step-by-step explanation:

[tex]\stackrel{50}{\sum \atop{n=1}}{\text{n}}[/tex]

First, we need to find the first term (a₁) and the last term (a₅₀)

a₁ = 1

a₅₀ = 50

Next, we need to input the information above into the Sum formula:

[tex]S_n=\dfrac{a_1+a_2}{2}\times n\\\\S_{50}=\dfrac{a_1+a_{50}}{2}\times 50\\\\.\quad =\dfrac{1+50}{2}\times 50\\\\.\quad =\dfrac{51}{2}\times 50\\\\.\quad =25.5\times 50\\\\.\quad =1275[/tex]

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