Question

Find the 10th term of G.P 512 ,256 ,128 ?

Answer 1

Answer:

a₁₀ = 1

Step-by-step explanation:

Given-----> 512 , 256 , 128 , ...................

To find ------> 10 th term of GP

Solution-----> 512 , 256 , 128 , ...............

Let , first term and common ratio of GP be a and r.

a = 512 , r = 256 / 512 , n = 10 , aₙ = ?

= 1 / 2

We know that, formula of nth term of GP is .

aₙ = a rⁿ⁻¹

=> a₁₀ = ( 512 ) ( 1 / 2 )¹⁰⁻¹

=> a₁₀ = ( 512 ) ( 1 / 2 )⁹

= 512 ( 1 / 512 )

=> a₁₀ = 1

Additional information---->

1) Formula of sum of n terms of GP .

sₙ = a ( rⁿ - 1 ) / ( r - 1 )

2) Formula of infinite term of GP

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