Question

In an Arithmetic Progression sixth term is one more than twice the thirdterm. The sum of the fourth and fifth terms is five times the second term.Find the tenth term of the Arithmetic Progression.​

Answer 1

Answer:

Let the first term be a and the common difference be d.

In AP, nth term = a + ( n - 1 )d

In the question,

= > 6th term = 2*3rd term + 1

= > a + ( 6 - 1 )d = 2[ a + ( 3 - 1 )d ] + 1

= > a + 5d = 2a + 4d + 1

= > d = a + 1

As well as,

= > 4th term + 5th term = 5*2nd term = > a + 3d + a + 4d = 5( a + d )

= > 2a + 7d = 5a + 5d

= > 2d = 3a

= > 2( a + 1 ) = 3a

= > 2a + 2 = 3a

= > 2 = a

Hence,

d = 2 + 1 = 3

Therefore,

= > 10th term,

= > a + 9d

= > 2 + 9(3)

= > 2 + 27

= > 29

10th term is 29