find find the indicated number of geometric means between each pair of numbers 16 and 81
Answers
3 geometric means between 16 and 81 can be 24 , 36 , 54 or -24 , 36 , -54
Given : Numbers 16 and 81
To Find : 3 geometric means between
Solution:
Geometric sequence
A sequence of numbers in which the ratio between consecutive terms is constant and called the common ratio.
a , ar , ar² , ... , arⁿ⁻¹
The nth term of a geometric sequence with the first term a and the common ratio r is given by: aₙ = arⁿ⁻¹
Sum is given by Sₙ = a(rⁿ - 1)/(r - 1)
Sum of infinite series is given by a/(1 - r) where -1 < r < 1
Need to insert 3 geometric means Hence total terms will be 5
16 , 16r , 16r² , 16r³ , 81
81 = 16r⁴
=> r⁴ = 81/16
=> r⁴ = ( ± 3/2)⁴
=> r = ± 3/2
Case 1 : r = 3/2
Geometric means are :
16 (3/2) = 24
16(3/2)² = 36
16(3/2)³ = 54
Geometric means are 24 , 36 , 54
Case 2 : r = -3/2
Geometric means are :
16 (-3/2) = -24
16(-3/2)² = 36
16(-3/2)³ = -54
Geometric means are -24 , 36 , -54
3 geometric means between 16 and 81 can be 24 , 36 , 54 or -24 , 36 , -54
Correct and complete Question is attached
Learn More:
In an infinite g.P. Each term is equal to three times the sum of all the ...
brainly.in/question/9079152
if s1,s2,s3...sp are the sum of infinite geometric series whose first ...
brainly.in/question/5796750
How to derive sum of n terms of an A.P? - Brainly.in
brainly.in/question/7849150
In an A.P if sum of its first n terms is 3n square +5n and it's Kth term ...
brainly.in/question/8236011
