Find four numbers in ap whose sum is 20

Asked by admin @ 17/08/2021 in Math viewed by 341 People

Find 4 numbers in ap whose sum is 20 and the sum of whose square is 120

Answered by admin @ 17/08/2021

Let the four numbers in A.P be a-3d, a-d,a+d,a+3d. ---- (1)

Given that Sum of the terms = 20.

= (a-3d) + (a-d) + (a+d) + (a+3d) = 20

4a = 20

a = 5. ---- (2)

Given that sum of squares of the term = 120.

= (a-3d)^2 + (a-d)^2 + (a+d)^2 + (a+3d)^2 = 120

= (a^2 + 9d^2 - 6ad) + (a^2+d^2-2ab) + (a^2+d^2+2ad) + (a^2+9d^2+6ad) = 120

= 4a^2 + 20d^2 = 120

Substitute a = 5 from (2) .

4(5)^2 + 20d^2 = 120

100 + 20d^2 = 120

20d^2 = 20

d = +1 (or) - 1.

Since AP cannot be negative.

Substitute a = 5 and d = 1 in (1), we get

a - 3d, a-d, a+d, a+3d = 2,4,6,8.

Hope this helps!

Find four numbers in ap whose sum is 20

Similar Questions

Find 4 numbers in ap whose sum is 20

Three numbers whose sum is 21 are in ap

Find three consecutive even numbers whose sum is 96

Find three consecutive even numbers whose sum is 234

Find two consecutive natural numbers whose sum is 75

Find two consecutive natural numbers whose sum is 63

Find three consecutive odd number whose sum is 147

Find three consecutive odd numbers whose sum is 147

Find the sum of first 20 natural numbers

Find the pythagorean triplet whose smallest number is 20

Find the sum of first 20 odd natural numbers

Find two consecutive natural numbers whose product is 20

Find four rational number between 3 and 4

Find the sum of all 11 terms of an ap

The sum of 3 numbers in ap is 15

Most viewed questions in Math

What is the value of x in the expression

Shubham is facing south and moves 30 km

Prachi excellence in mathematics class 7 solutions pdf free download

Oxford new enjoying mathematics class 7 solutions chapter 1

Survey of various types of bank accounts icse project

The town of p is located at point x

A clock gains 4 minutes after every 4 minutes

Running a tuck shop or canteen maths project pdf

Paul is sixteenth from the front of the row

The average weight of 20 teachers is 80 kg

The number 567 xy is completely divisible by 30

In a row of friends tiya occupies fifteenth place

What would $ mean if fat is coded as

Consider a 3 digit integer x with distinct digits

Rahul went to his mother's mother in law