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Let a1,a2 ,…. , a10 be in A.P. and h1,h...

Let `a_1,a_2` ,…. , `a_10` be in A.P. and `h_1,h_2` …. `h_10` be in H.P. If `a_1=h_1=2` and `a_10 = h_10 =3` , then `a_4 h_7` is :

A

2

B

3

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
D
Let d be the common difference of the A.P. Then,
`a_(10)=3rArra_(1)+9d=3rArr2+9d=3rArrd=(1)/(9)`.
`:." "a_(4)=a_(1)+3d=2+(1)/(3)=(7)/(3)`
Let D be the common difference of the A.P. `(1)/(h_(1)),(1)/(h_(2)), . . . .,(1)/(h_(10))`.
Then,
`h_(10)=3`
`rArr" "(1)/(h_(10))=(1)/(3)`
`rArr" "(1)/(h_(1))+9D=(1)/(3)rArr(1)/(2)+9D=(1)/(3)rArr9D=-(1)/(6)rArrD=-(1)/(54)`
`:." "(1)/(h_(7))=(1)/(h_(1))+6D=(1)/(2)-(1)/(9)=(7)/(18)rArrh_(7)=(18)/(7)`
Hence, `a_(4)h_(7)=(7)/(3)xx(18)/(7)=6`.
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