The first three terms of an arithmetic progression are t, 2t-1, 2t+4. Calculate the value of t.
To be an arithmetic progression,
(2t-1) - t = (2t+4) - (2t-1)
solve for t
(2t-1)-t=(2t+4)- (2t-1) 2t-1-t=2t+4-2t+1 collect like terms 2t-2t+2t=4+1+1 2t=6 divide 2 both side 2t/2=6/2 t=3
2.5
To find the value of t, we need to use the information given about the arithmetic progression. In an arithmetic progression, the difference between any two adjacent terms is constant.
Here, we can see that the first term is t, the second term is 2t-1, and the third term is 2t+4.
To find the common difference, we subtract the second term from the first term, and also subtract the third term from the second term. These differences should be the same.
Let's set up the equation:
(2t-1) - t = (2t+4) - (2t-1)
Simplifying the equation:
t - 1 = 2t + 4 - 2t + 1
On the right side, 2t and -2t cancel out. This leaves us with:
t - 1 = 5
Now, we can solve for t by isolating it:
t = 5 + 1
t = 6
Therefore, the value of t is 6.