Question

True or false:in a geometric sequence, the term a(n+1) can be smaller than the term a(n)

Answer 1

A(n) = current term

a(n + 1) = next term

in a geometric sequence, the next term comes from a product of the current term and the common ratio.

the common ratio can be any value, let's say use r = ½.

if the current term is say hmmm 40, the next term is 40*½ , or 20, so indeed, the next term is smaller.

Answer 2

True.  If the common ratio r is between 0 and 1 (for example), then each successive term will be smaller than the preceding term.