Let a1-a2-a3 be in A-P and let ap-aq-ar be in G-P- then aqap -

The correct option is C r qq p a _ 1 = p ^ th term a _ 2 = q ^ th term a _ 3 = r ^ th term a _ q a _ p =r= a _ r a _ q a _ q ...

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Quantitative Aptitude

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Let a1,a2,a...

Question

Let $a_{1}, a_{2}, a_{3}$ be in A.P and let $a_{p}, a_{q}, a_{r}$ be in G.P., then $\frac{a_{q}}{a_{p}} =$ _____.

\frac{r - p}{q - p}

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\frac{q - p}{r - q}

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\frac{r - q}{q - p}

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\frac{p - q}{p - r}

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Solution

The correct option is C $\frac{r - q}{q - p}$
$a_{1} = p^{t h}$ term
$a_{2} = q^{t h}$ term
$a_{3} = r^{t h}$ term
$\frac{a_{q}}{a_{p}} = r = \frac{a_{r}}{a_{q}} a_{q} = r a_{p} a_{r} = r a_{q} \frac{a_{q} {- a}_{r}}{a_{p} {- a}_{q}} = r$
Since $a_{1}, a_{2}, a_{3}$ are in $A P$
$\frac{[a + (q - 1) d] - [a + (r - 1) d]}{[a + (p - 1) d] - [a + (q - 1) d]} = r \frac{a + q d - d - a - r d + d}{a + p d - d - a - q d + d} = r \frac{d (q - r)}{d (p - q)} = r r = \frac{a_{q}}{a_{p}} = \frac{q - r}{p - q} = (\frac{r - q}{q - p})$

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Similar questions

Let $a_{1}, a_{2}, a_{3} . . . . . . . . .$ are in A.P such that $a_{p}$ , $a_{q}$ , $a_{r}$ are in both A.P and GP then $a_{q}$ : $a_{p}$ is equal to

Q. If

a_{1}, a_{2}, a_{3}, . . . . . . . . . .

are in AP then

a_{p}, a_{q}, a_{r}

are in AP if

p, q, r

are in:

Q. If

a_{1}

a_{2}

a_{3}

, ... are in AP then

a_{p}

a_{q}

a_{r}

are in AP if

p, q, r

are in

Q. Let

a_{1}, a_{2}, a_{3}, .

be an

A . P .

such that

\frac{a_{1} + a_{2} + . . . . + a_{p}}{a_{1} + a_{2} + a_{3} + . . . . + a_{q}} = \frac{p^{3}}{q^{3}}; p \neq q

. Then

\frac{a_{6}}{a_{21}}

is equal to:

Q. Let

a_{1}, a_{2}, a_{3} . . . .

be terms of an A.P. If

\frac{a_{1} + a_{2} + . . . . + a_{p}}{a_{1} + a_{2} + . . . . + a_{q}} = \frac{p^{2}}{q^{2}}, p \neq q

, then

\frac{a_{6}}{a_{21}}

equals

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Let a1,a2,a3 be in A.P and let ap,aq,ar be in G.P., then aqap=_____.

The correct option is C r−qq−pa1=pth terma2=qthterma3=rthtermaqap=r=araqaq=rapar=raqaq−arap−aq=rSince a1,a2,a3 are in AP[a+(q−1)d]−[a+(r−1)d][a+(p−1)d]−[a+(q−1)d]=ra+qd−d−a−rd+da+pd−d−a−qd+d=rd(q−r)d(p−q)=rr=aqap=q−rp−q=(r−qq−p)

Let $a_{1}, a_{2}, a_{3}$ be in A.P and let $a_{p}, a_{q}, a_{r}$ be in G.P., then $\frac{a_{q}}{a_{p}} =$ _____.