s is a geometric sequence find the value of x
Answers
Answer:
pls mark as brainliest and follow me especially if u r an one d fan!!!
Given : S is a geometric sequence
(√x + 1) , 1 and (√x -1) are first three terms of the sequence
To Find : Value of x
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
(√x + 1) , 1 and (√x -1) are first three terms of the sequence
=> r = 1/(√x + 1) = (√x -1) /1
1/(√x + 1) = (√x -1) /1
=> 1 = (√x + 1) (√x -1)
=> 1 = x - 1
=> x = 2
Hence x =2
a = (√2 + 1)
r = 1/(√2 + 1)
5th term of the sequence = ar⁴
= (√2 + 1) (1/(√2 + 1))⁴
= (√2 + 1) /(3 + 2√2)²
= (√2 + 1) /(17 + 12√2)
= (√2 + 1)(17 - 12√2) /(17 + 12√2) (17 - 12√2)
= -7 + 5√2
a = 5 , b = - 7
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