If the 7^{th} term of a H.P. is frac{1}{10} a | vedclass

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

Question

(D) Let the corresponding $A.P.$ have the first term $a$ and common difference $d$.Since the $n^{th}$ term of $H.P.$ is the reciprocal of the $n^{th}$

Vedclass · Accepted Answer

$\frac{1}{49}$

Vedclass · Answer

(D) Let the corresponding $A.P.$ have the first term $a$ and common difference $d$.Since the $n^{th}$ term of $H.P.$ is the reciprocal of the $n^{th}$ term of $A.P.$,we have:$7^{th}$ term of $A.P. = a + 6d = 10$$12^{th}$ term of $A.P. = a + 11d = 25$Subtracting the first equation from the second:$(a + 11d) - (a + 6d) = 25 - 10$$5d = 15 \Rightarrow d = 3$Substituting $d = 3$ into $a + 6d = 10$:$a + 6(3) = 10 \Rightarrow a + 18 = 10 \Rightarrow a = -8$The $20^{th}$ term of the $A.P.$ is $T_{20} = a + 19d = -8 + 19(3) = -8 + 57 = 49$.Therefore,the $20^{th}$ term of the $H.P.$ is the reciprocal of $49$,which is $\frac{1}{49}$.

If the $7^{th}$ term of a $H.P.$ is $\frac{1}{10}$ and the $12^{th}$ term is $\frac{1}{25}$,then the $20^{th}$ term is

Similar Questions

Let $E = x^{2017} + y^{2017} + z^{2017} - 2017xyz$ (where $x, y, z \geq 0$),then the least value of $E$ is

The $p^{th}$ term of the series $\left( 3 - \frac{1}{n} \right) + \left( 3 - \frac{2}{n} \right) + \left( 3 - \frac{3}{n} \right) + \dots$ will be

Write the seventh term of the following $GP$: $39366, 13122, 4374, 1458, \ldots$

$A$ person has two parents (father and mother),four grandparents,eight great-grandparents,and so on. Find the total number of ancestors the person has up to the $10^{th}$ generation.

The sum of the series $1 + \frac{4}{3} + \frac{10}{9} + \frac{28}{27} + \dots$ up to $n$ terms is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module