Determine whether each of the following is always, sometimes, or never true. If the answer is sometimes true, state the conditions under which it would be true.

Question

sn+1 - sn = an+1

Answer 1

is the n and n+1 a subscript?
If so, then we appear to be talking about the sequence of partial sums of a sequence.
So, take a look...
sn = a1 + a1 + ... + an
s_n+1 = a1 + a2 + ... + a_n + a_n+1
clearly, s_n+1 = s_n + a_n+1
so, s_n+1 - s_n = a_n+1 always