Question

in an ap sixth term is 1 more than twice the third term the sum of the 4 and 5 term is 5times the second term find 10th term if the ap​

Answer 1

★Given :

• In an Arithmetic Progression sixth term is one more than twice the third  term.
• The sum of the fourth and fifth terms is five times the second term.

★To find :

• The tenth term of the Arithmetic Progression.​

★Solution:

Let the AP is,

→a , a + d , a + 2d...

Where,

• a = first term
• d = common difference

Then,

• Second term = a  + d
• Third term = a + 2d
• Sixth term = a + 5d
• Fourth term = a + 3d
• Fifth term = a + 4d

Given that sixth term is one more than twice the third  term.Therefore,

Sixth term = third term + 1

➜a + 5d = 2(a + 2d) + 1

➜a + 5d = 2a + 4d  + 1

➜a-2a+5d-4d = 1

➜ d - a =  1

➜d =  a + 1-------(1)

Given,sum of the fourth and fifth terms is five times the second term.

Fourth term + fifth term = 5(second term)

➜(a + 3d) + (a + 4d)  = 5(a + d)

➜2a + 7d = 5a  + 5d

➜2d  = 3a

➜2(a + 1) = 3a

➜2a + 2  = 3a

➜ a = 2

Now substituting the value of 'a' in equation(1),

➜d = a + 1

➜2 + 1  = 3

Therefore,the common difference is 3.  

Now,

➜10th term = a + 9d

➜2 + 9(3)  

➜29

Hence,10th term of AP is 29.

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