Question

If second and fifth terms of a G.P. are 10 and 80 respt.. find the G.P.​

Answer 1

Given:

Second term of the Geometric Progression = 10

Fifth term of the Geometric Progression = 80

To find:

The Geometric Progression

Solution:

We know that nth term of a Geometric Progression is given by:

$tn = a {r}^{n - 1}$

For second term:

$10 = a {r}^{1}$

For fifth term:

$80 = a {r}^{4}$

This can be written as:

$80 = ar \times {r}^{3}$

Now putting the value we get:

$80 = 10 \times {r}^{3}$

${r}^{3} = 8$

$r = 2$

Since

$ar = 10$

$a = \frac{10}{r}$

$a = 5$

Thus a Geometric Progression will be formed with first term = 5 and common ratio= 2.

Therefore the geometric progression must be 5, 10, 15, 20....

The GP is 5, 10, 15, 20, 25....

Answer 2

Given : second and fifth terms of a G.P. are 10 and 80 respectively

To Find : GP

Solution:

Let say GP  is

a , ar , a r² , ar³ ,  a r⁴  

a = 1st term

a r = 2nd term = 10

a r⁴ = 5th term = 80

=> a r⁴ = 80

=> a r r³ = 80

=> 10 r³ = 80

=> r³ = 8  

=> r = 2

a r  = 10

=> a(2) = 10

=> a = 5

5 , 10 , 20 , 40 , 80  

a = 5 ,  r = 2

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