If t17 = 3 (t5) in an arithmetic progression, find t1 in terms of d.

t1 = 2d.

Step-by-step explanation:

The explicit formula for an arithmetic series is

The nth term tn = t1 + d (n - 1) where t1 = the first term, d = common difference and n = term number.

so t17 = t1 + 17d - d = t1 + 16d

and t5 = t1 + 5d - d = t1 + 4d

So t1 + 16d = 3 (t1 + 4d)

2t1 = 16d - 12d = 4d

t1 = 2d (answer).