# Math Help - Sequences

1. ## Sequences

Probably a silly question, but do all increasing sequences have a lower bound? I've been trying to work it out for a while and different people are telling me different things! Surely the lower bound will just be the first term, so when n=1? thanks in advance

2. Originally Posted by rainbow
Probably a silly question, but do all increasing sequences have a lower bound? I've been trying to work it out for a while and different people are telling me different things! Surely the lower bound will just be the first term, so when n=1? thanks in advance
If $\{a_n\}$ is an increasing sequence it means $a_1 < a_2< a_3 < a_4 < ...$. Therefore $a_1$ is a lower bound.