Question

Write four arithmetic sequences with 100 as the sum of the first four terms?

Answer 1

Let (a) (a+d) (a+2d) (a+3d) be the 4arthemetic series

then,S4 (4/2) (2a+(4-1)d)

100=2(2a+3d)

2a+3d=50........(1)

let d=2

then a= 22

therefore series is 22,24,26,28

put d=2,4,6.....16

Answer 2

Step-by-step explanation:

First number be n

Try with different A.P with different difference

1)With difference d=2

n+n+2+n+4+n+6=100

4n+12=100

n=88/4

n=22

Therefore first A.P 22,24,26,28….

2)With difference d=4

n+n+4+n+8+n+12=100

4n=100–24

4n=76

n=19

Second A.P 19,23,27,31…

3)With difference d=6

n+n+6+n+12+n+18=100

4n=100–36

4n=64

n=16

Third A.P 16,22,28,34…

4)With difference d=8

n+n+8+n+16+n+24=100

4n=100–48

4n=52

n=13

Fourth A.P 13,21,29,37