If the 5^{th} term of a Harmonic Progression | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) In a Harmonic Progression $(H.P.)$,the terms are the reciprocals of an Arithmetic Progression $(A.P.)$.Let the $A.P.$ have first term $a$ and comm

Vedclass · Accepted Answer

$1/89$

Vedclass · Answer

(A) In a Harmonic Progression $(H.P.)$,the terms are the reciprocals of an Arithmetic Progression $(A.P.)$.Let the $A.P.$ have first term $a$ and common difference $d$.The $5^{th}$ term of $H.P.$ is $1/45$,so the $5^{th}$ term of $A.P.$ is $a + 4d = 45 \dots (i)$.The $11^{th}$ term of $H.P.$ is $1/69$,so the $11^{th}$ term of $A.P.$ is $a + 10d = 69 \dots (ii)$.Subtracting $(i)$ from $(ii)$:$(a + 10d) - (a + 4d) = 69 - 45$$6d = 24 \implies d = 4$.Substituting $d = 4$ into $(i)$:$a + 4(4) = 45 \implies a + 16 = 45 \implies a = 29$.The $16^{th}$ term of the $A.P.$ is $a + 15d = 29 + 15(4) = 29 + 60 = 89$.Therefore,the $16^{th}$ term of the $H.P.$ is $1/89$.

If the $5^{th}$ term of a Harmonic Progression $(H.P.)$ is $1/45$ and the $11^{th}$ term is $1/69$,then its $16^{th}$ term is...

Similar Questions

If $H$ is the harmonic mean between $p$ and $q$,then the value of $\frac{H}{p} + \frac{H}{q}$ is

If $\cos (\theta-\alpha), \cos \theta$ and $\cos (\theta+\alpha)$ are in harmonic progression,then $2 \tan ^2 \theta=$

If ${a_1}, {a_2}, {a_3}, \dots, {a_n}$ are in $H.P.$,then the expression ${a_1}{a_2} + {a_2}{a_3} + \dots + {a_{n - 1}}{a_n}$ is equal to:

If $b + c, c + a, a + b$ are in $H.P.$,then $\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}$ are in

If ${x^a} = {x^{b/2}}{z^{b/2}} = {z^c}$,then $a, b, c$ are in

Vedclass Test Series

Exam Paper Generator

Online Exam Module