Home
Class 12
MATHS
Four numbers are in A.P. If their sum is...

Four numbers are in A.P. If their sum is 20 and the sum of their squares is 120, then the middle terms are

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|13 Videos

  • TEST PAPER

    ALLEN |Exercise CHEMISTRY SECTION-II|16 Videos

Similar Questions

Explore conceptually related problems

Find four consecutive terms in AP whose sum is 20 and the sum of whose squares is 120.

Three numbers in AP have the sum 18 and the sum of their squares is 180. Three those numbers in the increasing order.

In an A.P., the first term is 2 and the sum of the first five terms is one-fourth of the next five terms. Show that 20^("th") term is –112.

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

If the sum of p terms of an A.P. is q and the sum of q terms is p, then the sum of p+q terms will be

Soppose that all the terms of an arithmetic progression (AP) are natural numbers. If the ratio of the sum of the first seven terms to the sum of the first eleven terms is 6:11 and the seventh term lies between 130 and 140, then the common difference of this AP is

The first term of an AP is a and the sum of the first p terms is zero, show that the sum of its next q terms is (-a(p+q).q)/(p-1)

In a sequence of 21 terms the first 11 terms are in A.P. with common difference 2. and the lastterms are in G.P. with common ratio 2. If the middle tem of the A.P. is equal to themiddle term of the G.P., then the middle term of the entire sequence is

The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.

The digits of a positive integer, having three digit number are in A.P. and their sum is 15. The number obitained by reversing the digits is 594 less than the original number. Find the number.