Question

if 5th term of hp is1/45 ,11th term of hp is 1/69 then find 16th term

Answer 1

i hope it helps... follow me on instagram @jay_myself_103

Answer 2

Answer:

The 16th term of given H.P is

$\frac{1}{89}$

Step-by-step explanation:

Given that,

5th term of H.P is 1/45

We know that nth term of an HP is

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

Therefore,5th term is given as

$= = > \frac{1}{a + (5 - 1)d} = \frac{1}{45} \\ a + 4d = 45 - - (1)$

Now 11th term is given as

$\frac{1}{a + (11 - 1)d} = \frac{1}{69} \\ = > a + 10d = 69 - - (2)$

Solving equations (1) and (2),we get

$(2) - (1) = = > 6d = 24 = > d = 4 \\ (1) = = > a + 4(4) = 45 = > a = 29$

Therefore,we get the values of a and d as

a=29,d=4

Now the 16th term is given as

$a_{16} = \frac{1}{a + (16- 1)d} = \frac{1}{a + 15d} = \frac{1}{29 + 15(4)} = \frac{1}{89}$

Therefore,the 16th term of H.P is

$\frac{1}{89}$

#SPJ2