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 $|r|>1$.
- ABoth 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.
- CA is true but R is false.
- DA is false but R is true.
Answer
View full question & answer→(a) Both A and R are true and R is the correct explanation of A.
Explanation: Assertion: Given GP 4, 16, 64, ...
$\begin{array}{l}\therefore a=4, r=\frac{16}{4}=4>1 \\ \therefore S_6=\frac{4\left((4)^6-1\right)}{4-1}=\frac{4(4095)}{3}=5460\end{array}$
Hence, Assertion and Reason both are true and Reason is the correct explanation of Assertion.
Explanation: Assertion: Given GP 4, 16, 64, ...
$\begin{array}{l}\therefore a=4, r=\frac{16}{4}=4>1 \\ \therefore S_6=\frac{4\left((4)^6-1\right)}{4-1}=\frac{4(4095)}{3}=5460\end{array}$
Hence, Assertion and Reason both are true and Reason is the correct explanation of Assertion.