Advertisements
Advertisements
प्रश्न
The sum of three consecutive terms of an AP is 21 and the sum of the squares of these terms is 165. Find these terms
उत्तर
Let the required terms be (a-d) , a and ( a+d)
Then (a-d) + a+ (a+d) = 21
⇒ 3a = 21
⇒ a =7
Also , `(a - d)^2 + a^2 + (a + d)^2 = 165`
⇒ `3a^2 + 2d^2 = 165 `
⇒ `(3 xx 49 +2d^2) = 165`
⇒`2d^2 = 165 - 147 = 18`
⇒`d^2 = 9`
⇒ `d = +- 3`
Thus ,`a = 7 and d = +- 3`
Hence, the required terms are (4,7,10) or (10,7,4).
APPEARS IN
संबंधित प्रश्न
If (3y – 1), (3y + 5) and (5y + 1) are three consecutive terms of an AP then find the value of y.
If the sum of first n terms is (3n2 + 5n), find its common difference.
Find an AP whose 4th term is 9 and the sum of its 6th and 13th terms is 40.
If the common differences of an A.P. is 3, then a20 − a15 is
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
Q.12
How many terms of the series 18 + 15 + 12 + ........ when added together will give 45?
Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.
[Hint (iii) : These numbers will be : multiples of 2 + multiples of 5 – multiples of 2 as well as of 5]
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?
Measures of angles of a triangle are in A.P. The measure of smallest angle is five times of common difference. Find the measures of all angles of a triangle. (Assume the measures of angles as a, a + d, a + 2d)
