Question

The sum of first four terms of an Ap is 40 the ratio of the product of first and fourth term to secon and the third term is 2:3 find those term

Answer 1

Answer:4,8,12,16,20

Step-by-step explanation:

a(a+3d)/((a+d)(a+2d)=2/3

(a^2+3ad)/(a^2+2ad+ad+2d^2)=2/3

(a^2+3ad)(a^2+3ad+2d^2)=2/3

3(a^2+3ad)=2(a^2+3ad+2d^2)

3a^2+9ad=2a^2+6ad+4d^2

a^2+3ad=4d^2

a^2+3ad-4d^2

a^2+4ad-ad-4d^2

a(a+4d)-d(a+4d)

(a+4d)(a-d)=0

a+4d=0 a-d=0

a=-4d a=d

sum of four term =40

a+(a+d)+(a+2d)+(a+3d)=40

4a+6d=40

2a+3d=20

put a=d

2d+3d=20

5d=20

d=4

a=4

sequence is 4,8,12,16