Calculus
posted by Anonymous on .
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 +(n1)d
Tn = 1.75 + (n1)0.75
Tn = 1.75 + 0.75n 0.75
Tn = 0.75n + 1
T20....
T20 = 1.75 + (201)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.

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 + (n1)d
= 7/4 + (n1)(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