Question

what is the common difference of four terms in an AP suchthat the ratio of the product of the first fourth term to the second and third is 2:3 and the sum of all four term is 20

Answer 1

Answer:

Step-by-step explanation:

given ratio

a1a4/a2a3=2/3

a.a+3d/a+d.a+2d

let above equation be eq1

sum of four terms=a+a+d+a+2d+a+3d

=4a+6d=20

2a+3d=20

Answer 2

The common difference is ±1.

Step-by-step explanation:

Consider the provided information.

Let the four terms of the A.P are: $a-3d$, $a-d,a+d\ and\ a+3d$

The sum of all four term is 20.

$a-3d+a-d+a+d+a+3d=20\\4a=20\\a=5$

The ratio of the product of the first fourth term to the second and third is 2:3

$\dfrac{(a-3d)(a+3d)}{(a-d)(a+d)}=\dfrac{2}{3}\\\\\dfrac{(a^2-9d^2)}{(a^2-d^2)}=\dfrac{2}{3}$

Substitute a = 5.

$\dfrac{(25-9d^2)}{(25-d^2)}=\dfrac{2}{3}\\75-27d^2=50-2d^2\\25d^2=25\\d=\pm1$

Hence, the common difference is ±1.

#Learn more

The sum of three numbers in ap is 27 and the sum of their squares is293 then find the ap?

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