Question

If sum of 4 consecutive terms of A.P. is 50, greatest term is 4 times the last term then find the terms.​

Answer 1

Step-by-step explanation:

let the four consecutive terms be a-d , a ,a+d,a+2d,

This forms an A.P.

According to the first condition ,

a-d+a+a+d+a+2d= 50

4a+2d = 50 ....+d -d cancelled....1

According to the 2 condition,

a+2d = 4 ( a-d )

a+2d = 4a-4d

-3a + 6d = 0 ...2

multiple equ 1 by 3 and 2 by 4

12a+6d = 150 ...3

-12a + 18 d = 0 ....4 ...,.Adding equ 3. &4

24 d = 150

d = 150 \24

d= 6.25

substitute d= 25\4 in equ 1

4a+ 2( 25\4) = 50

4a + 12.5 =50

4a = 37.5

a= 9.4

a- d = 9.4 - 6 .25= 3.15

a= 9.4

a+ d = 9.4+ 6.25=15.65

a+2d =9.4+2(6.25)

=9.4+13

=22.4

answer the four consecutive number are 3.15,9.4,15.65,22.4