If the five terms are
x, x + 1, x + 2, x + 3, x + 4
x + x + 1 + x + 2 + x + 3 + x + 4 = 30
5x + 10 = 30
5x = 20
x = 4
The arithmetic sequence is 4, 5, 6, 7, 8
If the five terms are
x, x + 2, x + 4, x +6, x + 8
x + x + 2 + x + 4 + x + 6 + x + 8 = 30
5x + 20 = 30
5x = 30 – 20 = 10
x = 2
The arithmetic sequence is 2, 4, 6, 8, 10
If the five terms are
x, x + 3, x + 6, x + 9, x + 12
x + x + 3+ x+ 6 + x + 9 + x + 12 = 30
5X + 30 = 30
5x = 0
x = 0
The arithmetic sequence is 0, 3, 6, 9,12
The arithmetic sequences whose sum of first five terms give 30 are:
4, 5, 6, 7, 8, …………..
2, 4, 6, 8, 10, …………..
0, 3, 6, 9, 12, ………….
