Question

(1) Write three arithmetic sequences with 30 as the sum of the first five
terms​

Answer 1

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,

Step-by-step explanation: