Advertisements
Advertisements
प्रश्न
Show that `(a-b)^2 , (a^2 + b^2 ) and ( a^2+ b^2) ` are in AP.
उत्तर
The given numbers are `(a-b)^2 , (a^2 + b^2 ) and ( a+ b^2) `
Now,
`(a^2 + b^2 ) - (a-b)^2 = a^2 + b^2 - (a^2 -2ab + b^2 ) = a^2 + b^2 - a^2 + 2ab - b^2 = 2ab`
`(a+b)^2 - (a^2 + b^2) = a^2 + 2ab + b^2 - a^2 - b^2 = 2ab`
So, `(a^2 + b^2 ) - (a -b)^2 = (a + b)^2 - (a^2 + b^2 ) =2ab ` (Constant)
Since each term differs from its preceding term by a constant, therefore, the given numbers are in AP.
APPEARS IN
संबंधित प्रश्न
A contract on a construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs. 200 for the first day, Rs. 250 for the second day, Rs. 300 for the third day, etc., the penalty for each succeeding day being Rs. 50 more than for the preceding day. How much money does the contractor have to pay as a penalty if he has delayed the work by 30 days.
Find the sum of all 3 - digit natural numbers which are divisible by 13.
Which term of the AP ` 5/6 , 1 , 1 1/6 , 1 1/3` , ................ is 3 ?
What is the 5th term form the end of the AP 2, 7, 12, …., 47?
Draw a triangle PQR in which QR = 6 cm, PQ = 5 cm and times the corresponding sides of ΔPQR?
In an A.P. 19th term is 52 and 38th term is 128, find sum of first 56 terms.
Sum of 1 to n natural numbers is 36, then find the value of n.
If m times the mth term of an A.P. is eqaul to n times nth term then show that the (m + n)th term of the A.P. is zero.
Q.7
First four terms of the sequence an = 2n + 3 are ______.
