Although it is cheaper to go with a 10-year term, by design this assumes you won’t require life insurance after 10 years.  In addition, after 10 years your health may have declined and you may not get another well-priced 10-year term policy.
So there is a cost-saving going with a 10-year term policy, however, you are taking on an additional risk that you will still be healthy in 10 years.
A needs analysis should be completed when contemplating coverage to determine the right term for your specific needs. For example, if your mortgage is 25 years you would want to consider a Term 25 so the price is locked in and coverage is in place for the full length of your mortgage.