alleryIf $S_n=an^2+bn+c$, then the $n$th term $t_n$ of the sequence is
A$t_n=S_n+S_{n-1}$
B$t_n=S_n-S_{n-1}$
C$t_n=\dfrac{S_n}{n}$
D$t_n=S_{n+1}-S_n$
Answer & Solution
Correct answer: B. $t_n=S_n-S_{n-1}$
By definition, the $n$th term equals the sum of the first $n$ terms minus the sum of the first $(n-1)$ terms.
Therefore $t_n=S_n-S_{n-1}$.
**Option D gives the $(n+1)$th term, not the $n$th term.**
Keep practising Unit 2: Differentiation and Fundamental Derivative Rules
Browse all Unit 2: Differentiation and Fundamental Derivative Rules questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
$ in(180° - \theta)$ equals:A polynomial of degree 2 is called a:The common difference of the AP 3, 1, −1, −3, … is:If an AP has first term $a=6$ and common difference $d=-3$, which of the following is the The list $-1.0, -1.5, -2.0, -2.5, \ldots$ is an AP. What is its common difference?The square of any odd integer, when divided by 8, leaves remainderThe common difference of the AP 3, 1, −1, −3, … is:If the two lines are coincident (lie on top of each other), the pair has: