MCQ 11 Mark
Assertion $(A):$ The sum of first $6$ terms of the $GP 4, 16, 64,...$ is equal to $5460.$
Reason $(R):$ Sum of first $n$ terms of the $G.P$ is given by $S _{ n }=\frac{a\left(r^n-1\right)}{r-1}$,
where $a =$ first term $r =$ common ratio and $|r|>1$.
Reason $(R):$ Sum of first $n$ terms of the $G.P$ is given by $S _{ n }=\frac{a\left(r^n-1\right)}{r-1}$,
where $a =$ first term $r =$ common ratio and $|r|>1$.
- ✓Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
- BBoth $A$ 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: A.
Both $A$ and $R$ are true and $R$ is the correct explanation of $A$.
Assertion: Given $GP\ 4, 16, 64, ... $
$\therefore a=4, r=\frac{16}{4}=4>1$
$\therefore S_6=\frac{4\left((4)^6-1\right)}{4-1}$
$=\frac{4(4095)}{3}$
$=5460$
Hence, Assertion and Reason both are true and Reason is the correct explanation of Assertion.
$\therefore a=4, r=\frac{16}{4}=4>1$
$\therefore S_6=\frac{4\left((4)^6-1\right)}{4-1}$
$=\frac{4(4095)}{3}$
$=5460$
Hence, Assertion and Reason both are true and Reason is the correct explanation of Assertion.