Home
Class 12
MATHS
Let a1,a2,a3,... be in harmonic progress...

Let `a_1,a_2,a_3,...` be in harmonic progression with `a_1=5` and `a_(20)=25.` The least positive integer `n` for which `a_n<0`

A

22

B

23

C

24

D

25

Text Solution

Verified by Experts

The correct Answer is:
D
Plan nth term of HP, `t_(n) = (1)/(a + (n-1)n)`
Here, `a_(1) = 5, a_(20) = 25` for HP
`:. (1)/(a) = 5 and (1)/(a + 19d) = 25`
`rArr (1)/(5) + 19d = (1)/(25) rArr 19d = (1)/(25) - (1)/(5) = -(4)/(25)`
`:. d = (-4)/(19xx25)`
Since, `a_(n) lt 0`
`rArr (1)/(5) + (n-1) d lt 0`
`rArr (1)/(5) - (4)/(19xx25) (n-1) lt 0 rArr (n-1) gt (95)/(4)`
`rArr n gt 1 + (95)/(4) or n gt 24.75`
`:.` Least positive value of `n = 25`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let a_(1),a_(2),a_(3), . . . be a harmonic progression with a_(1)=5anda_(20)=25 . The least positive integer n for which a_(n)lt0 , is

If a_(1),a_(2),a_(3),"......" be in harmonic progression with a_(1)=5 and a_(20)=25 . The least positive integer n for which a_(n)lt0 is

If a_1,a_2,a_3 …. are in harmonic progression with a_1=5 and a_20=25 . Then , the least positive integer n for which a_n lt 0 , is :

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

If a_1,a_2,a_3,....a_n and b_1,b_2,b_3,....b_n are two arithematic progression with common difference of 2nd is two more than that of first and b_(100)=a_(70),a_(100)=-399,a_(40)=-159 then the value of b_1 is

If a_1,a_2,a_3,…….a_n are in Arithmetic Progression, whose common difference is an integer such that a_1=1,a_n=300 and n in[15,50] then (S_(n-4),a_(n-4)) is

Let a_1,a_2," ..."a_10 be a G.P. If a_3/a_1=25," then "a_9/a_5 equals

Let a_1,a_2,a_3…… ,a_n be in G.P such that 3a_1+7a_2 +3a_3-4a_5=0 Then common ratio of G.P can be