Answer:
62
Step-by-step explanation:
The general term of an arithmetic sequence with first term a1 and common difference d is ...
an = a1 +d(n -1)
The sum of n terms of an arithmetic sequence is ...
Sn = (2·a1 +d(n -1))(n/2)
Using these relations and the given values of a11 and s11, we can find a1 and d:
a11 = a1 +d(11 -1) = 32
S11 = (2·a1 +d(11 -1))(11/2) = 187
These simplify to ...
a1 +10d = 32
2a1 +10d = 34 . . . . multiply the second equation by 2/11
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Subtracting the first of these from the second, we get ...
a1 = 2
Then the common difference is ...
d = (32 -2)10 = 3
And the 21st term is ...
a21 = 2 +3(21 -1) = 62
The 21st term is 62.
