Formula for the arithmetic sequence -11,-3,5,

Remark

The difference is between any two terms. You should pick t3 and t4 which are both positive. That's easier to handle than a couple of minus signs.

d

t4 - t3 = d

13 - 5 = d

8 = d

a

the first term is - 11

Formula

t_n = a + (n-1)*d

t_n = -11 + (n-1)*8

Check

t_n = - 11 + (3-1)*8

t_3 = - 11 + 16

t_3 =  5 which it does.

Try t_5. It should be 21

t_5 = - 11 + (5 - 1)*8

t_5 = - 11 + 4 * 8

t_5 = -11 + 32

t_5 = 21

Answer

t_n = -11 + (n - 1)*8

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