Advertisements
Advertisements
प्रश्न
The sum of the squares of five consecutive natural numbers is 1455. Find the numbers.
उत्तर
Let the five consecutive integers be n, n + 1, n + 2, n + 3, n + 4 then,
n2 + (n + 1)2 + (n + 2)2 + (n + 3)2 + (n + 4)2 = 1455
n2 + n2 + 1+ 2n + n2 + 4n + 4 + n2 + 6n + 9 + n2 + 8n + 16 = 1455
[(a+b)2 = a2 + 2ab + b2]
5n2 + 20n + 30 = 1455
5n2 + 20n – 1425 = 0
5n2 + 20n – 1425 = 0
n2 + 4n – 285 = 0
∴ Compare with ax2 + 2bx + c = 0
`a = 1, b = 4, c = - 285`
b2 − 4ac = 42 − 4 × 1 × (−285)
= 16 + 1140 = 1156
n = `(-b ± sqrt(b^2- 4ac))/(2a)`
= `(-4 ± sqrt1156)/2`
= `(-4 ± 34)/2`
= `(-4 ± 34)/2` or `(-4 -34)/2`
`n = 15n -19`
As, `n = - 19` is not natural
Hence, the five consecutive numbers are 15,16, 17, 18, 19
APPEARS IN
संबंधित प्रश्न
State whether the following sequence is an A.P. or not?
1, 4, 7, 10, ………………..
For what value of k will k + 9, 2k – 1 and 2k + 7 are the consecutive terms of an A.P?
Write the first five terms of the sequence defined by `a_n = (–1)^(n-1) . 2^n`
Determine the 10th term from the end of the A.P. 4, 9, 14, …….., 254
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
-1.2, -3.2, -5.2, -7.2 …
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
`sqrt2, sqrt8, sqrt18, sqrt32 ...`
Following are APs or not? If they form an A.P. find the common difference d and write three more terms:
`sqrt3, sqrt6, sqrt9, sqrt12 ...`
If the 10th term of an A.P. is 52 and the 17th term is 20 more than the 13th term, find the A.P.
Write the expression an- ak for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which
11th term is 5 and the 13th term is 79.
Write the expression an- ak for the A.P. a, a + d, a + 2d, ... Hence, find the common difference of the A.P. for which
20th term is 10 more than the 18th term.
Which term of the A.P. 3, 10, 17, ... will be 84 more than its 13th term?
In an A.P., if the 12th term is −13 and the sum of its first four terms is 24, find the sum of its first ten terms ?
Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.
a + b, (a + 1) + b, (a + 1) + (b + 1), (a + 2) + (b + 1), (a + 2) + (b + 2), ...
Which of the following sequences is arithmetic progressions. For is arithmetic progression, find out the common difference.
12, 52, 72, 73, ...
Write the 25th term of an A.P. 12,16,20,24, .......
Find the first term and common difference of the Arithmetic Progressions whose nth term is given below
tn = 4 – 7n
The ratio of 6th and 8th term of an A.P. is 7:9. Find the ratio of 9th term to 13th term
If (m + 1)th term of an A.P. is twice the (n + 1)th term, then prove that (3m + 1)th term is twice the (m + n + 1)th term
1, 6, 11, 16 ...... Find the 18th term of this A.P.
The taxi fare after each km, when the fare is Rs 15 for the first km and Rs 8 for each additional km, does not form an AP as the total fare (in Rs) after each km is 15, 8, 8, 8,... Is the statement true? Give reasons.
