A statement Sn about the positive integers is given. Write statements S1, S2, and S3, and show that each of these statements is true. Show your work.
Sn: 2+5+8+...+(3n-1)=n(1+3n)/2
Sn = n(1+3n)/2
Therefore,
S1: 2 = 1(1 + 3(1))/2
S2: 2+5 = 2(1 + 3(2))/2
S3: 2+5+8 = 3(1 + 3(3))/2
They are all true/equivalent for S1, S2, and S3.
can you show me how you got those answers cause i have to show my work THANK YOU
Nevermind Thank you so much.
To show that each of the statements S1, S2, and S3 is true, we need to substitute different values of n into the statement Sn and verify that the equation holds true in each case.
S1: Substituting n = 1 into Sn:
2 + 5(1) - 1 = 1(1+3(1))/2
2 + 5 - 1 = 1(4)/2
6 = 4/2
6 = 2
The equation does not hold true, so S1 is not true.
S2: Substituting n = 2 into Sn:
2 + 5(2) - 1 = 2(1+3(2))/2
2 + 10 - 1 = 2(7)/2
11 = 14/2
11 = 7
The equation does not hold true, so S2 is not true.
S3: Substituting n = 3 into Sn:
2 + 5(3) - 1 = 3(1+3(3))/2
2 + 15 - 1 = 3(10)/2
16 = 30/2
16 = 15
The equation does not hold true, so S3 is not true.
None of the statements S1, S2, and S3 are true for the given statement Sn.