How do you find the 10th term of an arithmetic series?

Question

The 3rd term of an arithmetic series, A, is 19.
The sum of the first 10 terms of A is 290.
Find the 10th term of A.

Use #"S"_n = n/2 (2a+(n-1)d)#

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Answer 1 · 2018-05-18T11:09:54

#a_10=47#

So, we know that:
#a+2d=19#
#290=5(2a+9d)#

#a+2d=19#
#58=2a+9d#

We now use substituion to find the 10th term:
#a+2d=19#, #a=19-2d#
#2a+9d=58#

#2(19-2d)+9d=58#
#38-4d+9d=58#
#5d=20#
#d=4#

Putting this into 2 gives us:
#a+8=19#
#a=11#

#a_10=11+9(4)=47#