Six numbers are in AP such that their sum is 3 . The first term is 4 times the third term . Then , the fifth term is

Options

A. `-15`
B. `-3`
C. `9`
D. `-4`

Answer

D

Explanation

Let six numbers in AP be
`a-5d,a-3d,a-d,a+d,a+3d,a+5d`
`therefore a-5d+a-3d+a-d+a+d+a+3d+a+5d=3" "[because sum =3]`
`rArr 6a=3 rArr a=(1)/(2)`
Also , given `T_1=4T_3`, where `T_1T_3` are respectively , first and third terms of an AP.
`rArr a-5d=4(a-d)`
`rArr d=-3a=-(3)/(2)`
`therefore` The fifth term,
`a+3d=(1)/(2)+3(-(3)/(2))=(1)/(2)-(9)/(2)=-4` .