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.
Answers
Answer:
a6=1+2 (a3)
a+5d=1+2 (a+2d)
a+5d=1+2a+4d
5d-4d=2a-a+1
d=a+1
a4+a5=5 (a2)
a+3d+a+4d=5 (a+d)
2a+7d=5a+5d
7d-5d=5a-2a
2d=3a
2 (a+1)=3a
2a+2=3a
3a-2a=2
therefore a=2
we know that d=a+1, substitute value of 'a'
d=2+1
Hence d=3
a=2 d=3 a10=29
The AP is 2,5,8,11,14,17,20,23,26,29
Sixth term is 1 more than twice third term. a3= 8 and a6=17
Sum of fourth and fifth is five times second term. a4=11 a5= 14 11+14=25
a2=5 so 5×5=25
Step-by-step explanation:
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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