Advertisements
Advertisements
प्रश्न
Show that `(a-b)^2 , (a^2 + b^2 ) and ( a^2+ b^2) ` are in AP.
Advertisements
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
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
If (m + 1)th term of an A.P is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
Find the sum of the following arithmetic progressions:
`(x - y)/(x + y),(3x - 2y)/(x + y), (5x - 3y)/(x + y)`, .....to n terms
Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...
Find the sum of first 12 natural numbers each of which is a multiple of 7.
Determine the nth term of the AP whose 7th term is -1 and 16th term is 17.
The sum of first three terms of an AP is 48. If the product of first and second terms exceeds 4 times the third term by 12. Find the AP.
For an given A.P., t7 = 4, d = −4, then a = ______.
The first and the last terms of an A.P. are 8 and 350 respectively. If its common difference is 9, how many terms are there and what is their sum?
Find the sum of n terms of the series \[\left( 4 - \frac{1}{n} \right) + \left( 4 - \frac{2}{n} \right) + \left( 4 - \frac{3}{n} \right) + . . . . . . . . . .\]
Which term of the sequence 114, 109, 104, ... is the first negative term?
For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?
The first and last term of an A.P. are a and l respectively. If S is the sum of all the terms of the A.P. and the common difference is given by \[\frac{l^2 - a^2}{k - (l + a)}\] , then k =
Q.13
Q.16
Which term of the AP 3, 15, 27, 39, ...... will be 120 more than its 21st term?
Obtain the sum of the first 56 terms of an A.P. whose 18th and 39th terms are 52 and 148 respectively.
The middle most term(s) of the AP: -11, -7, -3,.... 49 is ______.
If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is ______.
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
