Advertisements
Advertisements
Question
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
Solution
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
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?
The sum of n, 2n, 3n terms of an A.P. are S1 , S2 , S3 respectively. Prove that S3 = 3(S2 – S1 )
Find the sum given below:
–5 + (–8) + (–11) + ... + (–230)
In an AP, given a = 7, a13 = 35, find d and S13.
Find the sum of all integers between 100 and 550, which are divisible by 9.
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.
Which term of the AP 3,8, 13,18,…. Will be 55 more than its 20th term?
Find an AP whose 4th term is 9 and the sum of its 6th and 13th terms is 40.
The sum of the first n terms of an AP is given by Sn = (3n2 – 4n). Find its
- nth term,
- first term and
- common difference.
The sum of the first n terms of an AP is `((3n^2)/2 + (5n)/2)`. Find its nth term and the 25th term.
The next term of the A.P. \[\sqrt{7}, \sqrt{28}, \sqrt{63}\] is ______.
Let there be an A.P. with first term 'a', common difference 'd'. If an denotes in nth term and Sn the sum of first n terms, find.
A man is employed to count Rs 10710. He counts at the rate of Rs 180 per minute for half an hour. After this he counts at the rate of Rs 3 less every minute than the preceding minute. Find the time taken by him to count the entire amount.
If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times, the least, then the numbers are
If the sums of n terms of two arithmetic progressions are in the ratio \[\frac{3n + 5}{5n - 7}\] , then their nth 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.
Find the sum of 12 terms of an A.P. whose nth term is given by an = 3n + 4.
Find the sum:
`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms
If Sn denotes the sum of first n terms of an AP, prove that S12 = 3(S8 – S4)
If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12th term.
