Home
Class 12
MATHS
Find the negative terms of the sequence ...

Find the negative terms of the sequence
`X_(n)=(.^(n+4)P_(4))/(P_(n+2))-(143)/(4P_(n))`

Text Solution

Verified by Experts

We have,
`x_(n)=(.^(n+4)P_(4))/(P_(n+2))-(143)/(4P_(n))`
`thereforex_(n)=((n+4)(n+3)(n+2)(n+1))/((n+2)!)-(143)/(4n!)`
`=((n+4)(n+3)(n+2)(n+1))/((n+2)(n+1)n!)-(143)/(4n!)`
`=((n+4)(n+3))/(n!)-(143)/(4n!)=((4n^(2)+28n-95))/(4n!)`
`because x_(n)` is negative
`therefore((4n^(2)+28n-95))/(4n!) lt 0`
which is true for n=1,2.
Hence, `x_(1)=(63)/(4) and x_(2)=-(23)/(8)` are two negative terms.
Promotional Banner

Similar Questions

Explore conceptually related problems

Number of positive terms in the sequence x_n=195/(4P_n)-(n+3p_3)/(P_(n+1)), n in N (here p_n=n! )

Find the indicated terms in each of the sequences whose n^(th) term is given: a_(n)= (n-1) (n+2)(n-3), a_(10)

Find the indicated terms in each of the sequences whose n^("th") terms are: a_n=(n(n-2))/(n+3),a_(20)

Find the indicated terms in each of the sequences whose n^("th") terms are: a_(n)=n^2/(2^n),a_(7)

Find the indicated terms in each of the sequences whose n^(th) term is given: a_(n)= (-1)^(n) (n^(2)-1), a_(13)

Find the value of n such that (""^(n)P_(4))/(""^(n-1)P_(4))=(5)/(3), n gt 4

Find the indicated terms in each of the sequences whose n^("th") terms are: a_(n) =4n-3,a_(17) ,a_(24)

Write the first five terms of each of the sequences whose n^(th) terms are: a_(n)= (n(n^(2) + 5))/(4)

Find the indicated terms in each of the sequences whose n^(th) term is given: a_(n)= n^(3)-2n, a_(8)

Find the indicated terms in each of the sequences whose n^(th) term is given: a_(n)= n^(2)-n+ 1, a_(5)