To find the sum of an arithmetic sequence, use the formula #S_n=(n(a_1+a_n))/2# where #S_n# is the sum of #n# terms, #a_1# is the first term in the sequence, and #a_n# is the #nth# term.
In this example, #a_1=34# and #a_n=2#. Notice that we don't have a value for #n#.
To find #n#, use the formula for an arithmetic sequence #a_n=a_1+(n-1)d# where #d# is the common difference between the terms (found by subtracting a previous term from a term).
In this example, #d=30-34=-4#
To find #n#, plug in #a_n=2#, #a_1=34# and #d=-4# into #a_n=a_1+(n-1)d#
#2=34+(n-1)(-4)#
#2=34-4n+4#
#-36=-4n#
#n=9#
Now, plug #n=9#, #a_1=34# and #a_n=2# into #S_n=(n(a_1+a_n))/2#
#S_n=(9(34+2))/2=162#
