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Assertion :The format of n^{th} term (T_n) of the sequence (2,

Question

Assertion :The format of $n^{t h}$ term $(T_{n})$ 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.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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

Assertion is correct but Reason is incorrect

Assertion is incorrect but Reason is correct

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Assertion :The format of

n^{t h}

term

(T_{n})

of the sequence

(ln 2, ln 4, ln 32, ln 1024.....)

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.

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Text solutionVerified

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.

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Question Text	Assertion :The format of $n^{t h}$ term $(T_{n})$ 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.
Answer Type	Text solution:1
Upvotes	150