Question

Assertion :The format of $n^{th}$ term $\left(T_n\right)$ of the sequence $(\ln 2,\ln 4,\ln 32,\ln 1024.....)$ is $a{n}^2+bn+c$. Reason: If the second successive differences between the consecutive terms of the given sequence are in G.P., then $T_n=a+bn+C{r}^{n-1}$, where a, b, c are constants and r is common ratio of G.P.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

$S=\ln 2+2\ln 2+5\ln 2+..........T_n$ .......... (i)
or $S=\ln 2+2\ln 2+5\ln 2+..........T_n$ .......... (ii)
(i) - (ii)
$\Rightarrow$ $T_n=\ln 2+2\ln 2+3\ln 2$ + .......... n terms
Now successive difference are in A.P.
$\Rightarrow T_n=a{n}^2+bn+c$
Statement - II is correct. But there is no relation between statement-1 and statemnt-2.