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)

your turn.

Answer 2

Let d=4 then sequence is
-2,2,6,10,14

Answer 3

Write four arithmetoc sequences with 100 as the sum of the first four terms.

Answer 4

Take first sequence as
x, x+1, x+2, x+3, x+4,
5x+10=30
5x=30-10
5x=20
x=20/5=4
Substitute the value of x
Then we get
4, 5, 6, 7, 8
Do the following like this
Then we get d= 1
Take second sequence as x, x+2, x+4, x+6, x+8
Then we get d = 2
Take third as x, x+3, x+6, x+9, x+12
Then we get d=3
We get the three are
4, 5, 6, 7, 8, 9
2, 4, 6, 8, 10
0, 3, 6, 9, 12