Question

The sum of first three terms of a G.P. is 6.2. find the common ratio if its first
term is 5.​

Answer 1

The value of r are $-\frac{6}{5}\ and\ \frac{1}{5}$.

Step-by-step explanation:

The sum of n terms of a GP is:

$S=\frac{a(r^{n}-1)}{r-1}$

Given:

n = 3

S = 6.2

a = 5

Compute the value of r as follows:

$S=\frac{a(r^{n}-1)}{r-1}$

$6.2=\frac{5(r^{3}-1)}{r-1}$

$\frac{31}{5}\times \frac{1}{5}=\frac{r^{3}-1^{3}}{r-1}$

$\frac{31}{25}=\frac{(r-1)(r^{2}+r+1)}{r-1}$

$\frac{31}{25}=r^{2}+r+1$

$r^{2}+r-\frac{6}{25}=0$

$25r^{2}+25r-6=0$

Factorize the last equation as follows:

$25r^{2}+25r-6=0\\25r^{2}+30r-5r-6=0\\5r(5r+6)-1(5r+6)=0\\(5r+6)(5r-1)=0$

Thus, the value of r are $-\frac{6}{5}\ and\ \frac{1}{5}$.

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Answer 2

Step-by-step explanation:

a + ar + ar² = 6.2

a(1+r+r²) = 6.2

1 + r + r² = 6.2/5

r² + r = 6.2/5 - 1

r² + r = 1.2/5 = 0.24

r² + r - 0.24 = 0

100r² + 100r - 24 = 0

25r² + 25r - 6 = 0

25r² + 30r - 5r - 6 = 0

5r(5r+6)-1(5r+6) = 0

(5r-1)(5r+6) = 0

r = 1/5 = 0.2 , r = -6/5