Multiple choice

Find the general term of a sequence, whose sum of n terms is given by $4n^2+3n$.

  1. $8n+1$
  2. $4n-2$
  3. $8n-1$
  4. $4n-1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The general term a_n is found by S_n - S_(n-1). Given S_n = 4n^2 + 3n, then S_(n-1) = 4(n-1)^2 + 3(n-1) = 4(n^2 - 2n + 1) + 3n - 3 = 4n^2 - 8n + 4 + 3n - 3 = 4n^2 - 5n + 1. Subtracting: (4n^2 + 3n) - (4n^2 - 5n + 1) = 8n - 1.

AI explanation

The formula to find the general term $t_n$ of a sequence when the sum of $n$ terms ($S_n$) is given is $t_n = S_n - S_{n-1}$. Substituting the given sum formula, we get $t_n = (4n^2 + 3n) - (4(n-1)^2 + 3(n-1))$. Expanding and simplifying this expression yields $4n^2 + 3n - 4n^2 + 8n - 4 - 3n + 3$, which equals $8n - 1$.

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