Advertisements
Advertisements
प्रश्न
Find the three numbers in AP whose sum is 15 and product is 80.
Advertisements
उत्तर
Let the required numbers be (a -d ),a and (a + d).
Then (a-d) +a + (a+d)=15
⇒ 3a =15
⇒a=5
Also, (a-d) . a . (a+d) = 80
⇒` a(a^2 - d^2 ) = 80`
⇒`5 (25 - d^2 ) = 80 `
⇒` d^2 = 25-16=9 `
⇒ `d =+- 3`
Thus a= 5 and `d = +- 3`
Hence, the required numbers are (2,5 and 8) or (8,5 and 2).
APPEARS IN
संबंधित प्रश्न
Find the sum of first 40 positive integers divisible by 6.
A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.
A small terrace at a football field comprises 15 steps, each of which is 50 m long and built of solid concrete. Each step has a rise of `1/4` m and a tread of `1/2` m (See figure). Calculate the total volume of concrete required to build the terrace.
[Hint: Volume of concrete required to build the first step = `1/4 xx 1/2 xx 50 m^3`]
If (m + 1)th term of an A.P is twice the (n + 1)th term, prove that (3m + 1)th term is twice the (m + n + 1)th term.
Find the sum of the following arithmetic progressions
`(x - y)^2,(x^2 + y^2), (x + y)^2,.... to n term`
Find the sum of all integers between 84 and 719, which are multiples of 5.
Find the sum of the first 15 terms of each of the following sequences having the nth term as
bn = 5 + 2n
Find the common difference of an AP whose first term is 5 and the sum of its first four terms is half the sum of the next four terms.
If the ratio of sum of the first m and n terms of an AP is m2 : n2, show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1) ?
There are 37 terms in an A.P., the sum of three terms placed exactly at the middle is 225 and the sum of last three terms is 429. Write the A.P.
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.
The sum of first 9 terms of an A.P. is 162. The ratio of its 6th term to its 13th term is 1 : 2. Find the first and 15th term of the A.P.
Write the expression of the common difference of an A.P. whose first term is a and nth term is b.
If 18, a, b, −3 are in A.P., the a + b =
If k, 2k − 1 and 2k + 1 are three consecutive terms of an A.P., the value of k is
In a Arithmetic Progression (A.P.) the fourth and sixth terms are 8 and 14 respectively. Find that:
(i) first term
(ii) common difference
(iii) sum of the first 20 terms.
The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.
First four terms of the sequence an = 2n + 3 are ______.
In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k.
In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.
