Advertisements
Advertisements
प्रश्न
In an A.P. sum of three consecutive terms is 27 and their product is 504, find the terms.
(Assume that three consecutive terms in A.P. are a – d, a, a + d).
Advertisements
उत्तर
Let the three consecutive terms of an A.P. be a – d, a, a + d.
According to the first condition
a – d + a + a + d = 27
3a = 27
a = `27/3`
a = 9
According to the second condition
(a – d) × (a) × (a + d) = 504
(9 – d) × 9 × (9 + d) = 504 .....(∵ a = 9)
(9 – d) (9 + d) = `504/9`
(9 – d) (9 + d) = 56
92 – d2 = 56 .....[∵ a2 – b2 = (a – b) (a + b)]
81 – d2 = 56
81 – 56 = d2
25 = d2
Taking square root on both sides
`sqrt25 = sqrt("d"^2)`
±5 = d
a = 9, d = 5
Three consecutive terms of an A.P. are
a – d = 9 – 5 = 4
a = 9
a + d = 9 + 5 = 14
4, 9, 14
a = 9, d = –5
a – d = 9 – (–5) = 9 + 5 = 14
a = 9
a + d = 9 + 5 = 14
14, 9, 4
∴ 4, 9, 14 or 14, 9, 4
APPEARS IN
संबंधित प्रश्न
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.
The sum of n, 2n, 3n terms of an A.P. are S1 , S2 , S3 respectively. Prove that S3 = 3(S2 – S1 )
Check whether -150 is a term of the A.P. 11, 8, 5, 2, ....
Find the sum given below:
34 + 32 + 30 + ... + 10
Find the sum of the first 15 terms of each of the following sequences having the nth term as
bn = 5 + 2n
Which term of the AP 3,8, 13,18,…. Will be 55 more than its 20th term?
If the pth term of an AP is q and its qth term is p then show that its (p + q)th term is zero
How many two-digit number are divisible by 6?
The angles of quadrilateral are in whose AP common difference is 10° . Find the angles.
Kargil’s temperature was recorded in a week from Monday to Saturday. All readings were in A.P. The sum of temperatures of Monday and Saturday was 5°C more than sum of temperatures of Tuesday and Saturday. If temperature of Wednesday was –30° celsius then find the temperature on the other five days.
Fill up the boxes and find out the number of terms in the A.P.
1,3,5,....,149 .
Here a = 1 , d =b`[ ], t_n = 149`
tn = a + (n-1) d
∴ 149 =`[ ] ∴149 = 2n - [ ]`
∴ n =`[ ]`
If the seventh term of an A.P. is \[\frac{1}{9}\] and its ninth term is \[\frac{1}{7}\] , find its (63)rd term.
If Sn denotes the sum of the first n terms of an A.P., prove that S30 = 3(S20 − S10)
For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?
The sum of first n odd natural numbers is ______.
A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.
If the sum of the first four terms of an AP is 40 and that of the first 14 terms is 280. Find the sum of its first n terms.
In an A.P. sum of three consecutive terms is 27 and their products is 504. Find the terms. (Assume that three consecutive terms in an A.P. are a – d, a, a + d.)
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
Find the sum of first 25 terms of the A.P. whose nth term is given by an = 5 + 6n. Also, find the ratio of 20th term to 45th term.
