MCQ 11 Mark
Assertion $(A):$ The sum of the first $n$ terms of an $A P$ is given by $S_n=3 n^2-4 n$. Then its $n$th term $a_n=6 n-7$
Reason $(R):$ nth term of an $AP,$ whose sum to $n$ terms is $S_n$, is given by $a_n=S_n-S_{n-1}$
Reason $(R):$ nth term of an $AP,$ whose sum to $n$ terms is $S_n$, is given by $a_n=S_n-S_{n-1}$
- ABoth $A$ and $R$ are true and $R$ is the correct explanation of $A$
- ✓Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Answer
View full question & answer→Correct option: B.
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A.$
$n^{th}$ term of an $AP$ be $a _{ n }= S _{ n }- S _{ n -1}$
$a_n=3 n^2-4 n-3(n-1)^2+4(n-1)$
$a_n=6 n-7$
So, both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
$a_n=3 n^2-4 n-3(n-1)^2+4(n-1)$
$a_n=6 n-7$
So, both $A$ and $R$ are true and $R$ is the correct explanation of $A$.