Progresión aritmética primer término14 / 19 segundo término 11 / 12, escribe los 5 siguentes terminos?

¡Hola!

Tenemos los siguientes datos en la progresión aritmética, veamos :

<img src="https://tex.z-dn.net/?f=a_1%5C%3A%28primer%5C%3At%5C%27ermino%29%20%3D%20%5Cdfrac%7B14%7D%7B19%7D%20" />

<img src="https://tex.z-dn.net/?f=a_2%5C%3A%28segundo%5C%3At%5C%27ermino%29%20%3D%20%5Cdfrac%7B11%7D%7B12%7D%20" />

<img src="https://tex.z-dn.net/?f=r%5C%3A%28raz%5C%27on%29%20%3D%5C%3A%3F" />

<img src="https://tex.z-dn.net/?f=a_3%5C%3A%28tercer%5C%3At%5C%27ermino%29%20%3D%5C%3A%3F" />

<img src="https://tex.z-dn.net/?f=a_4%5C%3A%28cuarto%5C%3At%5C%27ermino%29%20%3D%5C%3A%3F" />

<img src="https://tex.z-dn.net/?f=a_5%5C%3A%28quinto%5C%3At%5C%27ermino%29%20%3D%5C%3A%3F" />

<img src="https://tex.z-dn.net/?f=a_6%5C%3A%28sexto%5C%3At%5C%27ermino%29%20%3D%5C%3A%3F" />

<img src="https://tex.z-dn.net/?f=a_7%5C%3A%28s%5C%27eptimo%5C%3At%5C%27ermino%29%20%3D%5C%3A%3F" />

1) Paso : Encontrar la razón de una progresión aritmética, veamos :

<img src="https://tex.z-dn.net/?f=r%20%3D%20a_2%20-%20a_1" />

<img src="https://tex.z-dn.net/?f=r%20%3D%20%20%5Cdfrac%7B11%7D%7B12%7D%20-%20%5Cdfrac%7B14%7D%7B19%7D%20" />

MCM (12, 19) = 228

[img = 10]

[img = 11]

Vamos a aplicar la fórmula del término general de una Progresión Aritmética, para los 5 siguientes términosveamos :

[img = 12] * [img = 13]

[img = 14]

[img = 15]

[img = 16]

[img = 17]

MCM (19, 228) = 228

[img = 18]

[img = 19]

[img = 20] * [img = 21]

[img = 22]

[img = 23]

[img = 24]

[img = 25]

MCM (19, 228) = 228

[img = 26]

[img = 27]

[img = 28] * [img = 29]

[img = 30]

[img = 31]

[img = 32]

[img = 33]

MCM (19, 228) = 228

[img = 34]

[img = 35]

[img = 36] * [img = 37]

[img = 38]

[img = 39]

[img = 40]

[img = 41]

MCM (19, 228) = 228

[img = 42]

[img = 43] * [img = 44]

[img = 45]

[img = 46]

[img = 47]

[img = 48]

MCM (19, 228) = 228

[img = 49]

[img = 50]

[img = 51]

Por tanto, tenemos la siguiente progresión aritmética :

[img = 52]

¡Espero haberte ayudado, saludos.

DexteR!