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Nutka1998 [239]
1 year ago
11

What's the explicit rule for the sequence 3, -6, 12, -24, 48, ...?

Mathematics
2 answers:
Virty [35]1 year ago
7 0

Answer:

a_{n} = 3 (-2)^{n-1}

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

- 6 ÷ 3 = 12 ÷ - 6 = - 24 ÷ 12 = 48 ÷ - 24 = - 2

this indicates the sequence is arithmetic with explicit rule

a_{n} = a₁ (r)^{n-1}

where a₁ is the first term and r the common ratio

here a₁ = 3 and r = - 2 , then

a_{n} = 3 (-2)^{n-1}

777dan777 [17]1 year ago
4 0

Answer:

\sf \dfrac{-3}{2}(-2)^n

Step-by-step explanation:

Explicit formulas are used to represent all the terms of the geometric sequence with a single formula.

  \sf \boxed{\bf t_n = ar^{n-1}}

a is the first term.

r is the common ratio.

r = second term ÷ first term.

   3 , - 6 , 12, - 24, 48 ,........

a = 3

r = -6 ÷ 3 = -2

         \sf t_n = 3*(-2)^{(n-1)}\\\\

             \sf = 3*(-2)^{n}*(-2)^{-1}\\\\ =3*(-2)^n*\dfrac{-1}{2}\\\\= \dfrac{-3}{2}(-2)^n

Check:

\sf t_1 =\dfrac{-3}{2}*(-2)^1=\dfrac{-3}{2}*(-2) = 3\\\\\\t-2 = \dfrac{-3}{2}*(-2)^2 = \dfrac{-3}{2}*4=-6\\\\\\t_3=\dfrac{-3}{2}*(-2)^3=\dfrac{-3}{2}*(-8)=12

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