Question

the sum of four n numbers in a.p. is 28 and the product of firstand fourth is to thenproduct ofnsecond and third as 5:6 find the numbers

Answer 1

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Answer 2

Answer:

Let the four terms a-2d,a-d,a,a+d

We are given that the sum of four n numbers in a.p. is 28

So, $a-2d+a-d+a+a+d=28$

$4a-2d=28$

$2a-d=14$----1

Now we are given that the product of first and fourth is to then product of second and third as 5:6

$\frac{(a-2d)(a+d)}{(a-d)(a)}=\frac{5}{6}$

Substitute the value of d from 1

$\frac{(a-2(2a-14))(a+(2a-14))}{(a-(2a-14))(a)}=\frac{5}{6}$

a = 6, 8

At a = 6

d= 2(6)-14 = -2

a-2d= 6-2(-2)= 10

a-d=6-(-2)=8

a=6

a+d=6-2=4

At a = 8

d= 2(8)-14 = 2

a-2d= 8-2(2)= 4

a-d=8-(2)=6

a=8

a+d=8+2=10