Write the first five terms of each of the sequences in Questions 11 to 13 and obtain the corresponding series :
`a_(1)=-1, a_(n)=(a_(n-1))/(n),nge2`

Answer

N/a

Explanation

First term of given sequence `a_(1)=-1,`
and nth term of given sequence, `a_(n)=(a_(n-1))/(n)`
`therefore"At n =2, 2nd term "a_(2)=(a_(2-1))/(2)=(a_(1))/(2)=-(1)/(2),`
`"At n =3, 3rd term "a_(3)=(a_(3-1))/(3)=(a_(2))/(2)=(-(1)/(2))/(3)=-(1)/(6),`
`"At n =4, 4th term "a_(4)=(a_(4-1))/(4)=(a_(3))/(4)=(-(1)/(6))/(4)=-(1)/(24),`
`"At n =5, 5th term "a_(5)=(a_(5-1))/(5)=(a_(4))/(5)=(-(1)/(24))/(5)=-(1)/(120),`
Therefore, first 5 terms of given sequence are
`a_(1)=-1,a_(2)=(-1)/(2),a_(3)=-(1)/(6),a_(4)=-(1)/(24),a_(5)=-(1)/(120)`