Question

find the first term of GP whose second term is 2 and sum to infinity is 8
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Answer 1

Answer:

First term = 4

Step-by-step explanation:

Given---> Second term of GP = 2

Sum of infinite terms of GP = 8

To find---> First term of GP

Solution---> ATQ,

Second term = 2 , Sum of infinite terms = 8

a = 2

We know that formula of sum of infinite terms of GP

s( infinite ) = a / ( 1 - r )

=> 8 = a / (1 - r )

=> 8 ( 1 - r ) = a

Second term = 2

=> a r²⁻¹ = 2

=> a r = 2..........................(1)

Putting a = 8 ( 1 - r ) in it , we get

=> 8 ( 1 - r ) r = 2

=> 4 r ( 1 - r ) = 1

=> 4r - 4r² = 1

=> -4r² + 4r - 1 = 0

=> 4r² - 4r + 1 = 0

=> ( 2r )² - 2 ( 2r ) + (1)² = 0

=> ( 2r - 1 )² = 0

=> 2r - 1 = 0

=> 2r = 1

=> r = 1 / 2

Putting r= 1 / 2 in equation (1) , we get

ar = 2

=> a (1 / 2 ) = 2

=> a = 2 × 2

=> a = 4

Answer 2

Answer:

Step-by-step explanation:

The second term is 2.

The second term is actually a(r) where a is the first term and ‘r’ the common ratio.

So,a(r)=2 which means r=2/a —(1)

Sum of infinite terms of a GP is a/(1-r)=8

8–8r=a

-8(2/a)+8=a (Frm (1) )

8a-16=a^2

a^2-8a+16=0

a^2–4a-4a+16=0

a(a-4)-4(a-4)=0

(a-4)^2=0

Therefore a=4