Advertisements
Advertisements
Question
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.)
Advertisements
Solution
Let the three consecutive terms in an A.P. be a – d, a, and a + d.
According to the first condition,
sum of three consecutive terms is 27.
a – d + a + a + d = 27
∴ 3a = 27
∴ a = `27/3`
∴ a = 9 ..........(i)
According to the second condition,
the product of the three numbers is 504.
(a – d) a (a + d) = 504
∴ a(a2 – d2) = 504
∴ 9(92 – d2) = 504 ........[From(i)]
∴ 81 – d2 = `504/9`
∴ 81 – d2 = 56
∴ d2 = 81 – 56
∴ d2 = 25
Taking square root of both sides, we get
d = ±5
When d = 5 and a = 9,
a – d = 9 – 5 = 4
a = 9
a + d = 9 + 5 = 14
When d = – 5 and a = 9,
a – d = 9 – (– 5) = 9 + 5 = 14
a = 9
a + d = 9 – 5 = 4
∴ The three consecutive terms are 4, 9 and 14 or 14, 9 and 4.
APPEARS IN
RELATED QUESTIONS
The houses in a row numbered consecutively from 1 to 49. Show that there exists a value of x such that sum of numbers of houses preceding the house numbered x is equal to sum of the numbers of houses following x.
In an AP, given a = 2, d = 8, and Sn = 90, find n and an.
If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero
Find the sum of the first 51 terms of the A.P: whose second term is 2 and the fourth term is 8.
Determine the A.P. Whose 3rd term is 16 and the 7th term exceeds the 5th term by 12.
Find the sum of 28 terms of an A.P. whose nth term is 8n – 5.
If the 10th term of an AP is 52 and 17th term is 20 more than its 13th term, find the AP
Find the sum of first n even natural numbers.
Choose the correct alternative answer for the following question .
If for any A.P. d = 5 then t18 – t13 = ....
The nth term of an A.P., the sum of whose n terms is Sn, is
The term A.P is 8, 10, 12, 14,...., 126 . find A.P.
The 11th term and the 21st term of an A.P are 16 and 29 respectively, then find the first term, common difference and the 34th term.
What is the sum of an odd numbers between 1 to 50?
The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.
Find the sum:
`4 - 1/n + 4 - 2/n + 4 - 3/n + ...` upto n terms
Yasmeen saves Rs 32 during the first month, Rs 36 in the second month and Rs 40 in the third month. If she continues to save in this manner, in how many months will she save Rs 2000?
Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.
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.
The 5th term and the 9th term of an Arithmetic Progression are 4 and – 12 respectively.
Find:
- the first term
- common difference
- sum of 16 terms of the AP.
