Si en una progresión aritmética el primer término es a1=4, y la suma de los 42 primeros términos es S42=−2415, halla la diferencia d, y el término 59.

La suma de los primeros n términos de una suma aritmética es:

S(n) = n*(a₁ + aₙ)/2

donde el término enesimo de una progresion aritmética es:

aₙ = a₁ + n*d

Donde d es la diferencia entre dos términos consecutivos.

Para este caso sabemos que:

a₁ = 4

S(42) = -2415

Entonces podemos resolver la ecuación:

S(42) = 42*( a₁ + a₄₂)/2

         = 42*(4 + 4 + 42*d)/2

         = 42*(8 + 42*d)/2 = -2415

Ahora podemos resolver esta ecuación para encontrar el valor de d.

(8 + 42*d) = (2/42)*-2415 = -115

42*d = -115 - 8 = -123

 d = -123/42 ≈ -2.929

Y el término 59 va a ser:

a₅₉ = 4 + 59*d

     = 4 + 59*( -123/42) = -168.79

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.