if the geometric progression 3/32,3/16/3/8....and 96,48,24,.....have their nth term equal. find the value of n
Answers
value of n = 6 if geometric progression 3/32,3/16 , 3/8....and 96,48,24,.....have their nth term equal
Step-by-step explanation:
geometric progression 3/32,3/16 , 3/8....and 96,48,24,.....have their nth term equal
nth term of a GP is arⁿ⁻¹
a = First Term
r = common ratio
n = nth term
3/32,3/16 , 3/8....
a = 3/32
r = (3/16)/(3/32) = 2
nth term = (3/32)2ⁿ⁻¹
96 , 48 , 24
a = 96
r = 48/96 = 1/2
nth term = 96 * (1/2)ⁿ⁻¹
(3/32)2ⁿ⁻¹ = 96 * (1/2)ⁿ⁻¹
=> (1/32)2ⁿ⁻¹ = 32 * (1/2)ⁿ⁻¹
=> 2ⁿ⁻¹ * 2ⁿ⁻¹ = 32 * 32
=> 2ⁿ⁻¹ = 32
=> 2ⁿ⁻¹ = 2⁵
=> n - 1 = 5
=> n = 6
6th term of both = 3
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