Question

compute the 16th term of HP. if the 6th and 11th of HP are 10 and 18.​

Answer 1

16th term pf 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

Substituting d = - 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

Therefore the 16th term of HP is 90.