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.
Find the tenth term of the Arithmetic Progression.
10th board exam question
Karnataka please answer
Answers
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 say AP
a , a + d , a + 2d ..........
Sixth term = a + 5d
Third term = a + 2d
sixth term is one more than twice the third term.
=> a + 5d = 2(a + 2d) + 1
=> a + 5d = 2a + 4d + 1
=> d - a = 1
=> d = a + 1
sum of the fourth and fifth terms is five times the second term.
fourth term = a + 3d
Fifth term = a + 4d
Second term = a + d
(a + 3d) + (a + 4d) = 5(a + d)
=> 2a + 7d = 5a + 5d
=> 2d = 3a
=> 2(a + 1) = 3a
=> 2a + 2 = 3a
=> a = 2
d = a + 1 = 2 + 1 = 3
AP is
2 , 5 , 8 , 11 ............
10th term = a + 9d = 2 + 9(3) = 29
29 is 10th term of AP
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