For a G.P the ratio of the 7 th and the third terms is 16.The sum of 9 terms is 2555. What is the first term?
Answers
Given : For a G.P. the ratio of the 7th and the third terms is 16.
The sum of 9 terms is 2555.
To Find : the sequence.
Solution:
For a G.P. the ratio of the 7th and the third terms is 16.
aₙ = arⁿ⁻¹
a = first term
r = common ratio
n = number of term
7th term = ar⁶
3rd tern = ar²
ratio of the 7th and the third terms is 16.
=> ar⁶/ar² = 16
=> r⁴ = 16
=> r = ± 2
Sₙ = a(rⁿ - 1)/(r- 1)
The sum of 9 terms is 2555.
case 1 : r = 2
=> a(2⁹ - 1)/(2 - 1) = 2555
=> a (512 - 1) = 2555
=> a = 5
So sequence is
5 , 10 , 20 , 40 , 80 , 160 , 320 , 640 , 1280
case 2 : r = -2
=> a((-2)⁹ - 1)/(-2 - 1) = 2555
=> a (-512 - 1)/(-3) = 2555
=> 171a = 2555
=> a = 2555/171
So sequence is
2555/171 , -2* 2555/171 , 4 *2555/171 , - 8 *2555/171 and so on
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