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
Answer:
10
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)
10
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