Advertisements
Advertisements
Question
Show that `(a-b)^2 , (a^2 + b^2 ) and ( a^2+ b^2) ` are in AP.
Solution
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
RELATED QUESTIONS
Ramkali required Rs 2,500 after 12 weeks to send her daughter to school. She saved Rs 100 in the first week and increased her weekly saving by Rs 20 every week. Find whether she will be able to send her daughter to school after 12 weeks.
What value is generated in the above situation?
How many terms are there in the A.P. whose first and fifth terms are −14 and 2 respectively and the sum of the terms is 40?
Which term of the AP 21, 18, 15, …… is -81?
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 =
The sum of n terms of two A.P.'s are in the ratio 5n + 9 : 9n + 6. Then, the ratio of their 18th term is
Q.1
The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.
In an AP, if Sn = n(4n + 1), find the AP.
The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?
The nth term of an A.P. is 6n + 4. The sum of its first 2 terms is ______.
