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the sum of infinite number of terms of a decreasing G.P. is 4 and sum of the squares of its terms to infinity is 16/3,find the G.P

the sum of infinite number of terms of a decreasing G.P. is 4 and sum of the squares of its terms to infinity is 16/3,find the G.P

Grade:11

1 Answers

Arun
25750 Points
6 years ago
Dear Ramesh
 
a/(1-r) = 4
a = 4- 4r
 
Now
a²/(1-r²) = 16/3
3a² = 16 -16r²
3(16 + 16r² -32r) = 16 -16r²
48 + 48r² -96r = 16 -16r²
64r² -96r +32 = 0
2r² - 3r +1 = 0
(2r-1)(r-1) = 0
r = 1 and ½
r = 1 is neglected.
 
Hence r = 1/2 is accepted..(decreasing G.P.)
Now
a = 4 - 4*(1/2) = 4 - 2 = 2
 
Hence
G.P. will be
2, 1, 1/2, 1/4, .....
 
 
Regards
Arun (askIITians forum expert)

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