Class 10 Maths Chapter 5
10th Maths Arithmetic Progression Important Questions
Important Questions of Class 10 Maths
The common difference of two different arithmetic progressions are equal.The first term of the first progression is 3 more than the first term ofsecond progression. If the 7 th term of first progression is 28 and 8 th term of second progression is 29, then find the both different arithmetic progressions
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Let first term of first progression be a
And the first term of second progression be A
As per question : a=A+3 , and difference is same in both AP
And, seventh term=28(of first ap)
So, a+6d
We know a=A+3
So, a+6d..will become .A+3+6d=28
A+6d=25——(1)
And eight term =29(of second ap)
So, A+7d=29—–(2)
By elimination method in eq(1),(2)
A+6d=25—(1)
A+7d=29—(2)
————————-
-1d=-4
d=4.
Consider eq(1)
A+6d=25
A+6(4)=25
A+24=25
A=25-24
A=1
We know, a=A+3
a=1+3
a=4
1st AP : a+d, a+2d, a+3d, a+4d…
4 , 8 , 12 , 16……..
2nd AP : A+d, A+2d, A+3d, A+4d….
1 , 5 , 9 , 13…….
A+6d=28
=a+3+6d=28
a+6d=24–––––––1
a+7d=2a–––––––2
Solving 1 and 2
d=4and a=1
So the first ap : 4,8,12…………
And second ap:1, 5,9…..
A +6d= 28
A+3+6d = 28
A + 6d = 25…….1
A+ 7d = 29………2
Add 1 and 2
A = 1 D = 4
1st AP = 4,8,12,16……
2nd AP = 1,5,9,13
Let the first term of second AP = a
So, the first term of first AP = a + 3
7th term of first progression is 28
So, A + 6D = 28
⇒ a + 3 + 6D = 28
⇒ a + 6D = 25 … (1)
8th term of the second progression is 29
⇒ a + 7D = 29 … (2)
Solving (1) and (2), we have
D = 4 and a = 1
So, the first AP: 4, 8, 12 …
And the second AP: 1, 5, 9…