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

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

Explanation:

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

`a_2=4\\a_3=-12\\r=(a_(n+1))/(a_(n))=(-12)/(4)=-3`

`a_1=a_1/ r=4:(-3)=-\frac43\\\\a_n=-\frac43\cdot(-3)^(n-1)`