Determining Patterns?

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 :-)