Question

In H.p the 3rd term is 1/7 and 7 th term is 1/5 then show that the 15 th term is 1​ plss solve

Answer 1

Given:

In H.P. the $3^r^d$ term is 1/7 and $7^t^h$ term is 1/5

To show:

The $15^t^h$ term is 1​

Solution:

We know the formula for the $n^t^h$ term of an H.P. is:

$\boxed{\bold{T_n \:of \:H.P. = \frac{1}{a + (n - 1)d} }}$

According to the question, we get

∴ $t_3 = \frac{1}{a + (3 - 1)d} }}$

$\implies \frac{1}{7} = \frac{1}{a + (3 - 1)d} }}$

$\implies \frac{1}{7} = \frac{1}{a + 2d}$

$\implies 7 = a + 2d$

Also, we get

∴ $t_7 = \frac{1}{a + (7 - 1)d} }}$

$\implies \frac{1}{5} = \frac{1}{a + (7 - 1)d} }}$

$\implies \frac{1}{5} = \frac{1}{a + 6d}$

$\implies 5 = a + 6d$

On subtracting both the equations above, we get

a + 2d = 7

a + 6d = 5

-  -         -

-----------------

   -4d = 2

------------------

∴ $\bold{d = - \frac{1}{2}}$

On substituting the value of d in one of the equation, we get

$7 = a + (2\times \frac{-1}{2} )$

$\implies 7 = a -1$

$\implies a = 7 +1$

$\implies \bold{a = 8}$

Now,

The $15^t^h$ term is,

= $t_1_5$

= $\frac{1}{a + (15 - 1)d}$

= $\frac{1}{8 + (15 - 1)(\frac{-1}{2} )}$

= $\frac{1}{8 + (14)(\frac{-1}{2} )}$

= $\frac{1}{8 - 7}$

= $\boxed{\bold{1}}$

-----------------------------------------------------------------------------------------

Also View:

Find the 10th term of the Harmonic Progression 1/2, 1/4, 1/6?

https://brainly.in/question/24794778

In a Harmonic Progression 4/3, 3/2, 12/7. find 7th term?

https://brainly.in/question/1095044

10th term of a Harmonic Progression is third and fifth terms are respectively 1 and 1 by -5​

https://brainly.in/question/18792765

Answer 2

1234567890.@#$_&-+()/*"':;!?.★†‡«»›‹

Step-by-step explanation:

KAKAKA A AMA..ANANSNSNHSJSJWJWKWKKWKKKMKKLLKKKKKMNNANZJSNSSS SMSS

DD

F

G

HHKGLGOG

H

H

HIGOGKFMFFKEKED

• D.DJDJDJDJNDD KK S KM AK NA NA IN WSHAJNSHA ANANIA KM AMAISNSBNSJSS
• SNSJS
• SS
• SJDKJDJDRJIRF
• GGMIGKGMG BG GKH
• G
• GKRIJE GO GO GO GO DO GO DO SO WE TO ENF
• F
• F
• H
• J
• J

B

B

N

K

K

M

KKKK

KK

K

H

H

H

H

1. J
2. HH
3. H
4. H
5. B
6. H
7. J
8. J
9. J
10. J
11. J
12. J
13. J
14. J
15. J

J

J

K

J

J

J

KFIIDJDD

F

F