Question

The first term of a G.P is twice the common ratio .Find the sum of the first two terms of the progression if its infinity is 8​

Answer 1

Question:-

• The first term of a G.P is twice the common ratio . Find the sum of the first two terms of the progression if its sum of infinity is 8.

To Find:-

• Find the sum of two numbers.

Solution:-

Here ,

• a = 2r

• $\sf Sum \: of \: all \: terms = \dfrac { a } { 1 + r }$

Then ,

$\longrightarrow\sf \: \dfrac { 2r } { 1 - r } = 8$

$\longrightarrow\sf \: 2r = 8 - 8r$

$\longrightarrow\sf \: 8r + 2r = 8$

$\longrightarrow\sf \: 10r = 8$

$\longrightarrow\sf \: r = \cancel\dfrac { 8 } { 10 }$

$\longrightarrow\sf \: r = \dfrac { 4 } { 5 }$

Then ,

$\longrightarrow\sf \: a = 2r$

$\longrightarrow\sf \: a = 2 \times \dfrac { 4 } { 5 }$

$\longrightarrow\sf \: a = \dfrac { 8 } { 5 }$

Now ,

We have to find the sum of first two terms:-

$\longrightarrow\sf \: a ( 1 + r )$

$\longrightarrow\sf \: \dfrac { 8 } { 5 } ( 1 + \dfrac { 4 } { 5 } )$

$\longrightarrow\sf \: \dfrac { 8 } { 5 } \times \dfrac { 9 } { 5 }$

$\longrightarrow\sf \: \dfrac { 72 } { 25 }$

Hence ,

• Sum of all terms is $\sf \: \dfrac { 72 } { 25 }$

Answer 2

Question:-

The first term of a G.P is twice the common ratio . Find the sum of the first two terms of the progression if its sum of infinity is 8.

To Find:-

Find the sum of two numbers.

Solution:-

Here ,

a = 2r

$\sf Sum \: of \: all \: terms = \dfrac { a } { 1 + r }$

Then ,

$\longrightarrow\sf \: \dfrac { 2r } { 1 - r } = 8$

$\longrightarrow\sf \: 2r = 8 - 8r$

$\longrightarrow\sf \: 8r + 2r = 8$

$\longrightarrow\sf \: 10r = 8$

$\longrightarrow\sf \: r = \cancel\dfrac { 8 } { 10 }$

$\longrightarrow\sf \: r = \dfrac { 4 } { 5 }$

Then ,

$\longrightarrow\sf \: a = 2r$

$\longrightarrow\sf \: a = 2 \times \dfrac { 4 } { 5 }$

$\longrightarrow\sf \: a = \dfrac { 8 } { 5 }$

Now ,

We have to find the sum of first two terms:-

$\longrightarrow\sf \: a ( 1 + r )$

$\longrightarrow\sf \: \dfrac { 8 } { 5 } ( 1 + \dfrac { 4 } { 5 } )$

$\longrightarrow\sf \: \dfrac { 8 } { 5 } \times \dfrac { 9 } { 5 }$

$\longrightarrow\sf \: \dfrac { 72 } { 25 }$

Hence ,

Sum of all terms is $\sf \: \dfrac { 72 } { 25 }$