Home
Class 12
MATHS
Find four numbers in A.P. whose sum is 2...

Find four numbers in A.P. whose sum is 20 and the sum of whose squares is 120.

A

2, 4

B

4, 6

C

6, 8

D

8, 10

Text Solution

Verified by Experts

The correct Answer is:
B
Let the number are `a - 3d, a - d, a + d, a + 3d`
given, `a - 3d + a - d + a + d + a + 3d = 20 " " rArr 4a = 20 rArr a = 5`
and `(a - 3d)^(2) + (a - d)^(2) + (a + d)^(2) + (a + 3d)^(2) = 120 rArr 4a^(2) + 20d^(2) = 120`
`rArr 4 xx 5^(2) + 20 d^(2) = 120 " " rArr d^(2) = 1 rArr d = -+ 1`
Hence number 2,4,6,8 or 8,6,4,2
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Do yourself|3 Videos

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Do yourself 2|2 Videos

  • RACE

    ALLEN|Exercise Race 21|14 Videos

  • TEST PAPER

    ALLEN|Exercise CHEMISTRY SECTION-II|3 Videos

Similar Questions

Explore conceptually related problems

Find four numbers in A.P. whose sum is 28 and the sum of whose squares is 216.

Find the four numbers in A.P. whose sum is 20 and the sum of whose squares is 120.

Find the four numbers in A.P. whose sum is 20 and the sum of whose squares is 120.

Find three numbers in G.P. whose sum is 13 and the sum of whose squares is 91.

Find four number in an A.P. whose sum is 20 and sum of their squares is 120.

Find three numbers in A.P. whose sum is 9 and the sum of their squares is 35.

Find three numbers in A.P. whose sum is 9 and sum of whose cubes is 99.

Find three numbers in G.P. whose sum is 52 and the sum of whose products pairs is 624.

Find two positive numbers whose sum is 14 and the sum of whose squares is minimum.

Find two positive numbers whose sum is 15 and the sum of whose squares is minimum.