Step-by-step explanation:
could it be that you left out some past of the problem description ?
how I understand your rough text, we are looking for a geometric sequence, with the 3rd term = 12, and the multiplication factor being 2 (meaning that every term is the previous term times 2).
s3 = 12
f = 2
=>
s2 = 12/f = 12/2 = 6 (since the next term is the old term times 2, then the previous term is the new term divided by 2).
s1 = s2/2 = 6/2 = 3
s4 = s3 × f = 12 × 2 = 24
so, we see the structure, that
sn = sn-1 × 2
and sn-1 can then be expressed by sn-2 and so on, all the way to s1.
so, every term is the result of an equation based on s1.
s1 = 3
s2 = s1×2
s3 = s2×2 = s1×2×2
s4 = s3×2 = s2×2×2 = s1×2×2×2
[tex]sn = s1 \times {2}^{n - 1} [/tex]
[tex]sn = 3 \times {2}^{n - 1} [/tex]
that is the equation.
s10 is therefore
s10 = 3×2⁹ = 3×512 = 1536
explanation : see above.
