Question

For the Arithmetic sequence, determine the value of t1, and d. An explicit formula for the general term. And T20.

7/4, 1, 1/4, -1/2

I don't know how to do this the fraction way, but by doing this the decimal way, the common difference I got is -0.75. T1 would be 7/4.

Formula would be.

Tn = a +(n-1)d
Tn = 1.75 + (n-1)-0.75
Tn = 1.75 + -0.75n -0.75
Tn = -0.75n + 1

T20....

T20 = 1.75 + (20-1)-0.75
T20 = 1.75 + (19) - 0.75
T20 = 1.75 - 14.25
T20 = -12.5

I definitely got the last one wrong, please help.

Answer 1

common difference = 1 - 7/4 = 4/4 - 7/4 = -3/4 (you had -.75 correct!)
check: 1/4 - 1 = 1/4 - 4/4 = -3/4

t(n) = a + (n-1)d
= 7/4 + (n-1)(-3/4)
= 7/4 - (3/4)n + 3/4
= 10/4 - (3/4)n or t(n) = 5/2 - (3/4)n

Your error was in line:
Tn = 1.75 + -0.75n -0.75
should have been
Tn = 1.75 + -0.75n +0.75
= 2.5 - .75n , the same as mine

term(20) = a + 19d
= 7/4 + 19(-3/4)
= 7/4 - 57/4
= -50/4 or - 25/2