Question

Assertion : If sum of the first $n$ terma of an AP is given by $S_n=3n^2-4n$. Then ita $n^{\text{th}}$ term is $a_n=6n-7$.
Reason: $n^{\text{th}}$ term of an AP, whose sum to $n$ terma is $S_n$, is given by $a_n=S_n-S_{n}1$

• A. (c) Assertion (A) is true but reason (R) is false.
  
• B. (a) Both assertion (A) and reason (R) are true and reason $\left(R\right)$ is the correct explanation of assertion (A).
  
• C. (d) Assertion (A) is false but reason (R) is true.
• D. (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
  

Answer 1

The correct option is B (a) Both assertion (A) and reason (R) are true and reason $\left(R\right)$ is the correct explanation of assertion (A).


$n$th term of an $AP$,
$$a_n=S_n-S_{n-1}$$
$$\begin{array}{c}=3n^2-4n-3(n-1{)}^2+4(n-1)\\ =6n-7\end{array}$$
So, both $A$ and $R$ are correct and $R$ explains $A$. Thus (a) is correct option.