Question

What is the explicit formula of:
a. 1/3, -2/9, 4/27, -8/81
Also, how do you find it?

Answer 1

this looks like a Geometric Sequence in which you get the next term by multiplying by a constant factor

- 2/9 / 1/3 = -2/9 * 3 = -2/3
4/27 / -2/9 = 4/27 + 9/-2 = -2.3 also
and last term divided by 4/27 gives -2/3 as well so it is a GS with common ratio (r) = -2/3.

nth term an = a1r^(n-1) where a1 = frst term and r = common ratio.

so here it is 1/3 (-2/3)^(n-1) <===== explicit formula