Determining Patterns?

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Hello,

It bears repeating: you should have applied the well-known following formulas: "Hello", "Please" and "Thanks".
Anyway...

= = = = = = = = = = = = = = = = = =
Pattern: 24, 27, 30, 33, 36, 39, 42
Explanation in Words: Add 3 to the previous term
Algebraic recursive form:    uₐ₊₁ = 3 + uₐ
Algebraic explicit form:    uₐ = 3a + 21    for a≥1

= = = = = = = = = = = = = = = = = =
Pattern: 2, 6, 18, 54, 162, 486, 1,458
Explanation: Multiply previous term by three
Algebraic recursive form:    uₐ₊₁ = 3×uₐ
Algebraic explicit form:    uₐ = 2×3ª⁻¹    for a≥1

= = = = = = = = = = = = = = = = = =
Pattern: -10, -9, -7, -4, 0, 5, 11
Explanation: Add 1, add 2, add 3 etc...
Algebraic recursive form:    uₐ₊₁ = uₐ + a
Algebraic explicit form:    uₐ = -10 + a(a–1)/2    for a≥1

= = = = = = = = = = = = = = = = = =
Pattern: 1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64
Explanation: Divide previous term by 2
Algebraic recursive form:    uₐ₊₁ = uₐ/2
Algebraic explicit form:    uₐ = (½)ª⁻¹    for a≥1

Regards,
Dragon.Jade :-)...Show more