Math, asked by pratikshayadav205, 11 months ago

b) First term of a Geometric Progression is 2 and Common ratio is 2. How many
consecutive terms must be taken to give a sum of 2046?

Answers

Answered by rishu6845

Answer:

Step-by-step explanation:

Given---> First term of GP = 2 , Common ratio = 2

To find ---> Number of terms of GP whose sum is equal to 2046.

Solution---> ATQ , First term = 2

a = 2

Common ratio = 2

d = 2

Let sum of n terms of given GP is 2046 , so

a = 2 , d = 2 , Sₙ = 2046 , n = ?

Formula of sum of n terms of GP is

Sₙ = a ( rⁿ - 1 ) / ( r - 1 )

2046 = 2 ( 2ⁿ - 1 ) / ( 2 - 1 )

=> 2046 = 2 ( 2ⁿ- 1 ) / 1

=>2046/2 = 2ⁿ - 1

=> 1023 = 2ⁿ - 1

=> 1023 + 1 = 2ⁿ

=> 1024 = 2ⁿ

=> 2¹⁰ = 2ⁿ

Comoaring exponent we get

=> n = 10

Additional information--->

(1) Formula of nth term of GP

aₙ = a rⁿ⁻¹

(2) Formula of sum of infinite terms of GP

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

(3) GM between two numbers a and b = √(ab)

Answered by Aɾꜱɦ

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#answerwithquality #bal

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