How do you find the 10th partial sum of the arithmetic sequence #8, 20, 32, 33,...#?

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Answer 1 · 2017-05-14T15:50:33

#S_10=400#

For the sake of your question, let's assume your arithmetic sequences followed this pattern instead:
#8, 20, 32, 44# (not #33#)

Note the difference, #d=12#

The formula for the sum of #n# terms is

#S_n=n/2(a_1+a_n)#

Where #a_1=8# and #n=10#. This gives us

#S_10=10/2(8+a_(10))=5(8+a_(10))#

Next, find the formula for #a_n#

#a_n=a_1+(n-1)d#
#a_n=8+(n-1)12#
#a_n=8+12n-12#
#a_n=12n-4#

So, with #n=10#, we have #a_10=12(10-4)=72#

Therefore, #S_10=5(8+72)=400#