Question

find the 5 numbers in AP such that their sum that their sum is 20 and the product of 1st and last terms is 15​

Answer 1

Answer:

the number is A.P. are 3, 3.5 ,4 ,4.5 ,5

Step-by-step explanation:

What are 5 numbers in A.P. such that their sum is 20 and the product of the first and last is 15?

(a1 + a5) / 2 * 5 = 20 , a1 * a5

Let the five numbers in A.P. be

(a-2d),(a-d),a,(a+d),(a+2d)

Where d is the common difference of A.P.

It is given that addition of the number gives 20

So, (a-2d)+(a-d)+a+(a+d)+(a+2d)=20

Or, 5a=20

Or, a=4

And it is also given that product of first and last number is 15

So, (a-2d)*(a+2d)=15

Or, a²−4d²=15

Or, 16 - 4d²=15

This gives d= +0.5 or -0.5

Here -0.5 will not give then answer hence we will take d=+0.5

Hence the number is A.P. are 3, 3.5 ,4 ,4.5 ,5

Answer 2

Answer:

Let the five numbers in A.P. be

(a-2d),(a-d),a,(a+d),(a+2d)

Where d is the common difference of A.P.

It is given that addition of the number gives 20

So, (a-2d)+(a-d)+a+(a+d)+(a+2d)=20

Or, 5a=20

Or, a=4

And it is also given that product of first and last number is 15

So, (a-2d)*(a+2d)=15

Or, a^2−4d^2=15

Or, 16 - 4d^2=15

This gives d= +0.5 or -0.5

Here -0.5 will not give then answer hence we will take d=+0.5

Hence the number is A.P. are 3, 3.5 ,4 ,4.5 ,5