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
Advertisements
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
How many terms of the A.P. 65, 60, 55, .... be taken so that their sum is zero?
The first and the last terms of an AP are 8 and 65 respectively. If the sum of all its terms is 730, find its common difference.
Find the sum of the following APs.
`1/15, 1/12, 1/10`, ......, to 11 terms.
Find the sum of the first 11 terms of the A.P : 2, 6, 10, 14, ...
Find the sum of the first 40 positive integers divisible by 3
If the 8th term of an A.P. is 37 and the 15th term is 15 more than the 12th term, find the A.P. Also, find the sum of first 20 terms of A.P.
The sum of n natural numbers is 5n2 + 4n. Find its 8th term.
Find the 8th term from the end of the AP 7, 10, 13, ……, 184.
Find the first term and common difference for the following A.P.:
5, 1, –3, –7, ...
In an A.P. the first term is 8, nth term is 33 and the sum to first n terms is 123. Find n and d, the common differences.
Write 5th term from the end of the A.P. 3, 5, 7, 9, ..., 201.
If the sum of three consecutive terms of an increasing A.P. is 51 and the product of the first and third of these terms is 273, then the third term is
If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is
If 18th and 11th term of an A.P. are in the ratio 3 : 2, then its 21st and 5th terms are in the ratio
The sum of the first three terms of an Arithmetic Progression (A.P.) is 42 and the product of the first and third term is 52. Find the first term and the common difference.
In an A.P. a = 2 and d = 3, then find S12
In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k.
Solve the equation
– 4 + (–1) + 2 + ... + x = 437
Assertion (A): a, b, c are in A.P. if and only if 2b = a + c.
Reason (R): The sum of first n odd natural numbers is n2.
An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.
