a200 is the 200th term of the AP - Maths - Arithmetic Progressions

Question

a200 is the 200th term of the AP x, x+0 34, x+0 68, x+1 02 and
b200 is the 200th term of the AP Y, Y+0 34 , Y+0 68, Y+1 02
IT IS GIVEN THAT X+Y=7 and a200 -b200 = 0 124 find x & y

Harleen Birdi · Accepted Answer

Dear Student!!

Here is the answer to your query.

Given two A. P.'s :

I) x, x + 0.34, x + 0.68, x + 1.02, ...

II) y, y + 0.34, y + 0.68, y + 1.02, ...

a₂₀₀ is the 200^th term of A. P. I & b₂₀₀is the 200^th term of A. P. II.

It is given that: x + y = 7 and a₂₀₀– b₂₀₀= 0.124.

For I^st A.P. :

a₁ = x, a₂ = x + 0.34

Common difference (d) = a₂ – a₁ = (x + 0.34) – x = 0.34

For II^nd A.P.:

b₁ = y, b₂ = y + 0.34

Common difference (D) = b₂ – b₁ = (y + 0.34) – y = 0.34

Now, a₂₀₀– b₂₀₀= 0.124

⇒ a + 199d – (b + 199D) = 0.124

⇒ a + 199 (0.34) – b – 199 (0.34) = 0.124

$\Rightarrow x - y = 0.124 (P utting a = x & b = y) ... (1) Also, x + y = 7 ... (2)$

Adding (1) & (2),

2x = 7.124

$\Rightarrow x = 3.562$

Putting the value of x in (2), we get y = 7 – x = 7 – (3.562) = 3.438

Hence, x = 3.562 and y = 3.438.

Cheers..!!

a200 is the 200th term of the AP x, x+0.34, x+0.68, x+1.02....... and b200 is the 200th term of the AP Y, Y+0.34 , Y+0.68, Y+1.02 IT IS GIVEN THAT X+Y=7 and a200 -b200 = 0.124 find x & y

a200 is the 200th term of the AP x, x+0.34, x+0.68, x+1.02....... and b200 is the 200th term of the AP Y, Y+0.34 , Y+0.68, Y+1.02

IT IS GIVEN THAT X+Y=7 and a200 -b200 = 0.124 find x & y