Answers

  • Brainly User
2016-06-25T23:00:41+08:00
General formula:

an = a₁ + (n-1) (d)

Given sequence:  25, 32, 39, 46, ...

a₁ = 25      d = 7 (common difference)

an = 25 + (n-1)(7)
an = 25 + 7n - 7
an = 7n + 25 - 7
an = 7n + 18

ANSWER:   a_{n} = 7n + 18

Check:
a₁ = 25
a₁ = 25 + (1-1)(7)
a₁ = 25 + (0)(7)
a₁ = 25 + 0
a₁ = 25  (True)

a₄ = 46
a₄ = 25 + (4-1) (7)
a₄ = 25 + (3)(7)
a₄ = 25 + 21
a₄ = 46  (True)

To find the 100th term:
a₁₀₀ = ?
a₁₀₀ = 25 + (100-1) (7)
a₁₀₀ = 25 + (99)(7)
a₁₀₀ = 25 + 693
a₁₀₀ = 718

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