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before the first of an arithmetic sequence is -8 and the 16th term is 67, a. find the common difference b. find the 25th term

Respuesta :

Answer:

d = 5 , a₂₅ = 112

Step-by-step explanation:

(a)

The nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₁ = - 8 and a₁₆ = 67 , then

a₁ + 15d = 67

- 8 + 15d = 67 ( add 8 to both sides )

15d = 75 ( divide both sides by 15 )

d = 5

(b)

a₂₅ = - 8 + (24 × 5) = - 8 + 120 = 112

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