Question

If the second term of a geometric sequence is 4 and the third term is –12, find the
explicit formula.
an= 3•(4/3) n-1
an =-4/3•(-3)n-1
an=-3•(-4/3) n-1
an = 4/3 •(3)n-1

Answer 1

Answer:

            $\bold{a_n=-\frac43\cdot(-3)^{n-1}}$

Step-by-step explanation:

The formula of a geometric sequence:  aₙ = a₁ rⁿ⁻¹

$a_2=4\\a_3=-12\\r=\frac{a_{n+1}}{a_{n}}=\frac{-12}{4}=-3$

$a_1=a_1\div r=4:(-3)=-\frac43\\\\a_n=-\frac43\cdot(-3)^{n-1}$