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Find the PA whose third term is 8 and whose ninth term is 26.

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Answer to a math question Find the PA whose third term is 8 and whose ninth term is 26.

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Sigrid
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115 Answers
1. El término general de una progresión aritmética (P.A.) está dado por:

a_n = a + (n-1)d

2. Dado que el tercer término es 8:

a + 2d = 8

3. Dado que el noveno término es 26:

a + 8d = 26

4. Resolver el sistema de ecuaciones:

a + 2d = 8

a + 8d = 26

5. Restando la primera ecuación de la segunda:

(a + 8d) - (a + 2d) = 26 - 8

6d = 18

d = 3

6. Sustituyendo el valor de \( d \) en la primera ecuación:

a + 2(3) = 8

a + 6 = 8

a = 2

Respuesta final:

a = 2

d = 3

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