compute the 16th term of HP. if the 6th and 11th of HP are 10 and 18.
Answers
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Answer :
16 th term of HP is 90.
Step-by-step explanation:
If a,b,c,... are in AP then 1/a,1/b,1/c,... are in HP.
The H.P is written in terms of A.P are given below:
6th term of A.P = a + 5 d = 1/10 ...(1)
11th term of A.P = a + 10 d = 1/18 ...(2)
Now , Do (2) - (1) , we get,
=> 5 d = 1/18 - 1/10
=> 5 d = -2/45
=> d = -2 /225
sub. this in (1) , we get ,
=> a = 13/90
To find 16th term, we can write the expression in the form,
a+15d = (13/90) – (2/15) = 1/90
Thus, the 16th term of an H.P = 1/16th term of an A.P = 90
Therefore, the 16th term of the H.P is 90.
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16th term of HP is 90.
Step-by-step explanation:
6 th term of HP = 10
Using nth term of HP formula
a(n) = 1 / [ a + ( n - 1 )d ]
=> a(6) = 1 / [ a + 5d ] = 10
=> 1 / 10 = a + 5d --- Eq( 1 )
11th term of HP = 18
=> a(11) = 1 / ( a + 10d) = 18
=> 1 / 18 = a + 10d --- Eq( 2 )
Subtracting Eq( 1 ) from Eq( 2 )
=> 1 / 18 - 1 / 10 = a + 10d - a - 5d
=> ( 10 - 18 ) / 180 = 5d
=> - 8 / 180 = 5d
=> - 2 / 45 = 5d
=> - 2 / 225 = d
Substitutingd = - 2 / 225 in ( 1 )
=> 1 / 10 = a + 5( - 2 / 225 )
=> 1 / 10 = a - 2 / 45
=> 1 / 10 + 2 / 45 = a
=> ( 45 + 20 ) / 450 = a
=> 65 / 450 = a
=> 13 / 90 = a
16th term of HP = a(16) = 1 / [ a + 15d ]
= 1 / [ 13/90 + 15( - 2 / 225 ) ]
= 1 / [ 13/90 - 2/ 15 ]
= 1 / [ ( 13 - 12 ) / 90 ]
= 1 / ( 1 / 90 )
= 90