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STD 11 - 8. sequence and series — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 8. sequence and series4 Marks
Question
Suppose the sequence $a_1, a_2, a_3, \ldots$ is a n arithmetic progression of distinct numbers such that the sequence $a_1, a_2, a_4, a_8, \ldots$ is a geometric progression. The common ratio of the geometric progression is
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Answer

a
(a)

We have, $a_1, a_2, a_3, \ldots, a_n$ in an $AP$ and $a_1, a_2, a_4, a_8$ in GP.

Let $a_1=a, a_2=a+d, a _3=a+2 d$ and $a_1$, $a_2, a_4, a_8$ are in $GP$.

Let common ratio is $r$.

$\therefore \quad a_1=a, a_2=a r, a_4=a r^2, a_8=a r^3$

$\therefore a+ d =a r, a+3 d=a r^2, a+7 d=a r^3$

$\Rightarrow \quad 2 d =a r(r-1), 4 d=a r^2(r-1)$

$\Rightarrow \quad r=2$

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