Question

The sum of first three terms of a G. P. is
49/15
and their product is 1, then find
the common ratio and the terms of G. P.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The common ratio of the G. P. is $\frac{3}{5}$.

The terms of G. P. are $\frac{5}{3}$, 1, $\frac{3}{5}$, ......

Step-by-step explanation:

The general form of the geometrical progression is given by

$a, ar, ar^{2}, ar^{3}, ar^{4}, ....$

Where r ≠ 0 is the common ratio

and a ≠ 0 is the initial value

Let's consider the first three terms of the G. P. as

$a, ar, ar^{2}$

The sum of the first three terms of G. P. is given by

$a+ ar+ ar^{2}= \frac{49}{15}$

The product of the first three terms of G. P. is given by

$(a)(ar)( ar^{2})= 1$

Consider,

$a^{3}r^{3}=1$

$(a)(r)=1$ $(a=\frac{1}{r})$

$a+ ar+ ar(r)= \frac{49}{15}$

$a+ 1+ 1(r)= \frac{49}{15}$

$a+r = \frac{34}{15}$

$\frac{1}{r}+r = \frac{34}{15}$

$15r^{2} -34r+15=0$

The roots of the equation are $r = \frac{3}{5}$ or $r=\frac{5}{3}$

$a=\frac{1}{r}$

$a = \frac{5}{3}$

The common ratio of the G. P is $r=\frac{3}{5}$

The terms of G. P. are

$\frac{5}{3}$, 1, $\frac{3}{5}$, ......