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Six numbers are in AP such that their s...

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

A

-15

B

-3

C

9

D

-4

Text Solution

Verified by Experts

The correct Answer is:
d
Let six number in Ap be
` a- 5d, a-3d, a-d , a+d, a+3d, a+5d`
` :. A - 5d +a-3d+a -d +a+d +a+3d +a +5d =3`
`[ :' "sum" =3]`
` rArr 6a= 3 rArr a=1/2`
Also , given `T_(1) = 4T_(3)` are respectively , first and third terms of an AP.
`rArr a- 5d = 4(a-d)`
`rArr d = -3a = -3/2`
` :. "The fifth term" a +3d =1/2 +3(-3/2)`
` = 1/2 -9/2=-4`
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