Arithmetic Series
Formulae
- \(S_{n}=\frac{n}{2}(2a+(n-1)d)\)
- \(S_{n}=\frac{n}{2}(a+l)\)
- Bottom formula can only be used if we know the value of the last term in the sequence.
Finding out terms in a sequence
- To quickly find out the number of terms in an arithmetic sequence, take away the first term from the last term, divide by the difference between consecutive terms, and add 1.
Arithmetic Series
- \(3+7+11+14\dots\)
\(n=20\)
\(a=3\)
\(d=4\)
\(10(6+80-4)\)
\(820\)
- \(2+6+10\dots\)
\(n=15\)
\(a=2\)
\(d=4\)
\(7.5(4+60-4)\)
\(450\) - \(30+27+24\dots\) 40 terms
\(n=40\)
\(a=30\)
\(d=-3\)
\(20(60-120+3)\)
\(-1140\) - \(5+1+-3+-7\) 14 terms
\(n=14\)
\(a=5\)
\(d=-4\)
\(7(10-56+4)\)
\(-294\) - \(5+7+9+\dots+75\)
\(n=36\)
\(d=2\)
\(a=5\)
\(18(80)=1440\)