Discouragement is quieter than despair and tends to arrive in the middle of something worth doing. These passages were chosen for that specific stretch.
Notice how many of them are addressed to a group rather than to one person. Encouragement in scripture is usually something people do for each other.
Which suggests the most useful response to a discouraging week is often not a verse at all, but telling one person you are having one. These are for the stretch before you can face doing that.
1 Thessalonians 5 : 11
Wherefore comfort yourselves together, and edify one another, even as also ye do.
Encouragement here is a task handed to the people around you, not something you are expected to manufacture alone at your lowest.
Hebrews 10 : 24
And let us consider one another to provoke unto love and to good works:
Provoke is the old, stronger word, and it is being used positively. It describes the friend who will not let you quietly give up.
Galatians 6 : 9
And let us not be weary in well doing: for in due season we shall reap, if we faint not.
The condition is attached plainly: if we faint not. This is a verse about the gap between sowing and harvest, which is where most discouragement happens.
Deuteronomy 31 : 6
Be strong and of a good courage, fear not, nor be afraid of them: for the LORD thy God, he it is that doth go with thee; he will not fail thee, nor forsake thee.
Spoken to a people about to lose their leader and go on without him. The courage asked for is for the stretch after the person you relied on is gone.
Romans 15 : 4
For whatsoever things were written aforetime were written for our learning, that we through patience and comfort of the scriptures might have hope.
An argument for why old writing helps at all: patience and comfort, in that order. It is the clearest statement of what a page like this is for.
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