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Let a(1), a(2),"…..",a(10) be in A.P. an...

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
Given that `a_(1),a_(2),"……"a_(10)` be un AP.
Let d be the common difference of AP.
`:. d=(a_(10)-a_(1))/(10-1)`
`d=(3-2)/(9) " " [" given that " a_(1)=h_(1)=2 " and " a_(10)=h_(10)=3]`
`d=(1)/(9)`
`:.a_(4)=a_(1)+3d=2+(3)/(9)=2+(1)/(3)=(7)/(3)`
Now, `h_(1),h_(2),"......,"h_(10)` be in HP.
So, common difference of respective AP.
`D=((1)/(h_(10))-(1)/(h_(1)))/(10-1)=((1)/(3)-(1)/(2))/(9)=(-1)/(9xx6)-(-1)/(54)`
So, `(1)/(h_(7))=(1)/(h_(1))+6D " " implies (1)/(lambda_(7))=(1)/(2)+6((-1)/(54))=(1)/(2)-(1)/(9)`
`(1)/(h_(7))=(7)/(18)" " implies h_(7)=(18)/(7)`
So, `a_(4)h_(7)=(7)/(3)xx(18)/(7)=6`.
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