If 9 HM-s are inserted between 2 - 3- the general term of i th HM isA- 2- i 1-90B- 2-i-60C- 1-2-i-60D- 1-2-i-90

The correct option is C Let H_1, H_2, ........ H_9 be HM's inserted ⇒ 2, H_1, H_2,——— H_9, 3 are in H.P Common difference of corresponding A.P. is D = ...

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Standard XI

Mathematics

Sum of n Terms in AP

If 9 HM's are...

Question

If 9 HM's are inserted between 2 & 3, the general term of i^th HM is

2 - i( )

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Solution

The correct option is C
-

Let $H_{1}$ , $H_{2}$ , ........ $H_{9}$ be HM's inserted

$\Rightarrow$ 2, $H_{1}$ , $H_{2}$ ,--------- $H_{9}$ , 3 are in H.P

Common difference of corresponding A.P. is

D = $\frac{a - b}{(n + 1) a b}$ = $\frac{2 - 3}{10 \times 6}$ = $\frac{- 1}{60}$

We know $\frac{1}{H_{i}}$ = $\frac{1}{a}$ + iD

= $\frac{1}{2}$ + i. $\frac{- 1}{60}$ = $\frac{1}{2}$ - $\frac{i}{60}$

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If 9 HM's are inserted between 2 & 3, the general term of ith HM is

The correct option is C - Let H1, H2, ........ H9 be HM's inserted ⇒ 2, H1, H2,--------- H9, 3 are in H.P Common difference of corresponding A.P. is D = a−b(n+1)ab = 2−310×6 = −160 We know 1Hi = 1a + iD = 12 + i. −160 = 12 - i60

If 9 HM's are inserted between 2 & 3, the general term of i^th HM is