Topic explanation

Standard explanation

If last term l is given, Sn = n(a+l)/2. Find n first from an = l if needed. Word problems: seats in a theatre, logs in a stack (school).

Key points

• average of ends * n
• S_n = n/2 * (2a+(n-1)d)
• also n/2 * (a1+a_n)
• do not drop /2
• WITH ENDS: If last term l is given, Sn = n(a+l)/2. Find n first from an = l if needed. Word problems: seats i
• WITH ENDS: If last term l is given, S_n = n(a+l)/2.
• WHAT — WITH ENDS: If last term l is given, Sn = n(a+l)/2. Find n first from an = l if needed. Word problems: seats i
• WHY — Why it matters: This rule is a separate learning unit inside sum of an arithmetic series. It can be defined, applied

Labelled diagram