If the 2nd, 5th and 9th term of A.P. are in G.P. then find the common ratio of G.P.

\frac{8}{5}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{4}{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{4}{3}$
$a_{2}, a_{5}, a_{9}$ of $A . P .$ are in $G . P .$
${(a_{5})}^{2} = a_{2} a_{9}$
${(a + 4 d)}^{2} = (a + d) (a + 8 d)$
$a^{2} + {16 d}^{2} + 8 a d = a^{2} + 9 a d + {8 d}^{2}$
${8 d}^{2} = a d$
$a = 8 d$
$r = \frac{a_{5}}{a_{2}}$
$r = \frac{a + 4 d}{a + d}$
$r = \frac{16 d}{12 d}$
$r = \frac{4}{3}$

Suggest Corrections

Similar questions

If the $2^{n d}, 5^{t h} a n d 9^{t h}$ terms of non-constant A.P. are in G.P., then the common ratio of this G.P. is:

2^{n d}, 5^{t h}

9^{t h}

2 n d 5 t h

9 t h

A . P

G . P

G . P

If the $2^{n d}$ term of a G.P. is $1$ and $5^{t h}$ term is $\frac{1}{125}$ , then the $9^{t h}$ term will be ____.

2^{n d}, 3^{r d}

6^{t h}

A . P .

G . P .

G . P .

Join BYJU'S Learning Program