9th grade math honors
posted by Anonymous .
suppose t(1)=91 and 67 is another term of an arithmetic sequence, with. What is the equation of the nth term of the sequence if there are n terms between these two?

Tn = a + (n1)d
T1 = 91 = a
If there are n terms between 91 and 67, then 67 = Tn+2
Tn+2 = 91 + (n+1)d = 67
d = 24/(n+1)
Tn = 91 + (n1)*24/(n+1)
Check: suppose there are 3 terms between 91 and 67. Then d = 24/4 = 6
T: 91 (85 79 73) 67 61 ...