Question

write three arithmetic sequences with 30 as the sum of the first five terms?

Answer 1

sum(5) = (5/2)(2a + 4d) = 30 
2a + 4d = 12 
a + 2d = 6 

a = 6-2d 

so we can assign any value to d 
e.g. d = 7 
then a = 6-14 = -8 
one possible sequence is: 
-8 , -1, 6, 13, 20 
(their sum is 30) 

let d = 3 
a = 6-6 = 0 
terms are: 
0, 3, 6, 9, 12 
(their sum is 30) 
I think it is helpful for you

Answer 2

Answer:

Let's take the first term as 'x'

Then the sequence will be as follows

x , x+d , x+2d , x+3d , x+4d,...

Sum of first five terms,

x+(x+d)+(x+2d)+(x+3d)+(x+4d) = 30

5x+10d = 30

5(x+2d) = 30

x+2d = 30/5

x+2d = 6

x = 6-2d

when d= 1,

x = 6- 2×1

= 4

when d= 2,

x = 6-2×2

= 6-4

=2

when d= 3,

x = 6-2×3

= 6-6

= 0

Therefore the three arithmetic sequence with 30 as the sum of the first five terms are:-

1 ) 4,5,6,7,8,...

2) 2,4,6,8,10,...

3) 0,3,6,9,12,...

I think it will be the simplest way to solve this problem..