Home
Class 12
MATHS
If four nos. in decreasing A.P, a, b, c,...

If four nos. in decreasing A.P, a, b, c, d have their sum as 20 & sum of squares is 120 then a-b+c-d is

Text Solution

Verified by Experts

The correct Answer is:
D
Decreasing A.P.
`therefore a gt b gt c gt d`
`implies 4A=20" "A=5`
also, `(A+3D)^(2)+(A+D)^(2)+(A-D)^(2)+(A-3D)^(2)=120`
`implies D=+1" "therefore a=8,b=6,c=4,d=2" "therefore (a+c)-(b+d)=12-8=4`.
Promotional Banner

Similar Questions

Explore conceptually related problems

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

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

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

Find four numbers in A.P whose sum is 8 and the sum of whose squares is 196 .

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

If four numbers in A.P. are such that their sum is 50 and the greatest number is 4 times the least, then the numbers are (a) 5, 10, 15, 20 (b) 4, 10, 16, 22 (c) 3, 7, 11, 15 (d) none of these

The product of two numbers is 120 and the sum of their squares is 289. The sum of the numbers is a. 20 b. 23 c. 169 d. none of these