The sum of the first $n$ terms of a series is $S_n = 3n^2 + n$. Find the $n$th term.
A$6n - 2$CORRECT
B$6n + 2$
C$3n + 1$
D$6n$
GCEFurther MathematicsSequences and Series2019
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Why the answer is A, and why the others tempt you.
The nth term T_n = S_n - S_(n-1) = [3n²+n] - [3(n-1)²+(n-1)] = 3n²+n - 3(n²-2n+1) - n+1 = 3n²+n-3n²+6n-3-n+1 = 6n-2. Option B (6n+2) results from a sign error when expanding, and option C misapplies the formula entirely.
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