If `2lambda,lambda` and `[lambda^(2)-14],lambda in R-{0}` and `[*]` denotes the gratest integer function are the first three terms of a GP in order, t

Question

If `2lambda,lambda` and `[lambda^(2)-14],lambda in R-{0}` and `[*]` denotes the gratest integer function are the first three terms of a GP in order, t

If `2lambda,lambda` and `[lambda^(2)-14],lambda in R-{0}` and `[*]` denotes the gratest integer function are the first three terms of a GP in order, then the 51th term of the sequence, `1,3lambda,6lambda,10lambda,"….",` is
A. 5104
B. 5304
C. 5504
D. 5704

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - B
`:.2lambda,lambda,[lambda^(2)-14]` are oin GP, then
`lambda ^(2)=2lambda[lambda^(2)-14]`
`implies (lambda)/(2)=[lambda^(2)-14]`
`:.lambda ` must be an evenm integer
Hence, `lambda=4`
Now, reqyured sequence `1,12,24,40,"….."`
or `1,4(1+2),4(1+2+3),4(1+2+3+4),"...."`
`:. 51th " term "=4(1+2+3+"...."+51)`
`=4*(51)/(2)(1+51)=4*51*26=5304`