QJEEAdv08Ma5d7a: JEE Advanced 2008 Mathematics - Class 11 JEEAdv08Ma5d7a Solution: Suppose four distinct positive numbers are in G.P. Let .…

Question

Verified Solution • 2025–26 Session moderate

Suppose four distinct positive numbers

{a_1},\,{a_{2\,}},\,{a_3},\,{a_4}\,

are in G.P. Let

{b_1} = {a_1},{b_2} = {b_1} + {a_2},\,{b_3} = {b_2} + {a_{3\,\,}}\,\,\,and\,\,\,{b_4} = {b_3} + {a_4}

.

STATEMENT-1: The numbers ${b_1},\,{b_{2\,}},\,{b_3},\,{b_4}\,$ are neither in A.P. nor in G.P. and

STATEMENT-2 The numbers ${b_1},\,{b_{2\,}},\,{b_3},\,{b_4}\,$ are in H.P.

A STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
B STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C STATEMENT-1 is True, STATEMENT-2 is False
D STATEMENT-1 is False, STATEMENT-2 is True

Accepted Answer

Given, $a_1,a_2,a_3,a_4$ are in G.P.

Then, $b_1,b_2,b_3,b_4$ are the numbers.

$a_1,a_1+a_2,a_1+a_2+a_3,a_1+a_2+a_3+a_4$ or $a,a+ar,a+ar+ar^2,a+ar+ar^2+ar^3$

Clearly above numbers are neither in A.P. nor in G.P. and hence statement 1 is true.

Also, ${1 \over a},{1 \over {a + ar}},{1 \over {a + ar + a{r^2}}},{1 \over {a + ar + a{r^2} + a{r^3}}}$ are not in H.P.

$\therefore$ $b_1,b_2,b_3,b_4$ are not in H.P.

$\therefore$ Statement 2 is false.

Step-by-Step Verified Solution