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Progresiones aritméticas: conceptos y ejercicios

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Conceptos y fórmulas AR

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Progresiones aritméticas: conceptos y ejercicios
 

Progresiones aritméticas: conceptos y ejerciciosOnline version

Conceptos y fórmulas AR

by ronny ruiz
1

¿Qué define a una progresión aritmética?

2

¿Cómo se llama la diferencia entre términos consecutivos en una progresión aritmética?

3

Dado a1=5 y d=3, ¿cuál es a4?

4

¿Cuál es la fórmula de la suma de una progresión aritmética S_n?

5

Si a1=4, d=-2, ¿a5?

6

¿Qué representa a_n en una progresión aritmética?

7

Si la progresión tiene a1=7 y a10=31, ¿d?

8

¿Qué indica la suma parcial S_n cuando n crece?

9

¿Una progresión aritmética puede tener d=0?

10

¿Qué significa que d sea positivo?

Explicación

La d fija: a_{n+1}-a_n = d, constante.

La diferencia común se denota por d.

a_n = a1 + (n-1)d; a4 = 5+3*3=14.

Forma clásica: S_n = n/2 (a1 + a_n) y a_n = a1 + (n-1)d.

a5 = 4 + (5-1)(-2) = 4 - 8 = -4; corregir: correcta es -4. (Ajuste)

a_n es el término en la posición n.

a10=a1+(10-1)d →31=7+9d → d=24/9=8/3 ≈ 2.67; si se espera entero, usar datos diferentes. Ajuste: d= (31-7)/9 = 24/9 = 8/3.

S_n acumula la suma de los primeros n términos.

Con d=0, todos los términos son iguales a a1.

d>0 implica crecimiento constante entre términos.

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