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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?

• 9th grade math honors -

Tn = a + (n-1)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 + (n-1)*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 ...

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