Answer:
t(n) = 1 +6(n -1)
Step-by-step explanation:
The general term of an arithmetic sequence with first term t(1) and common difference d is given by the formula ...
t(n) = t(1) +d(n -1)
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Using the two given values of n and t(n), we can find the unknown parameters.
13 = t(3) = t(1) +d(3 -1) = t(1) +2d
67 = t(12) = t(1) +d(12 -1) = t(1) +11d
Subtracting the first equation from the second, we get ...
(67) -(13) = (t(1) +11d) -(t(1) +2d)
54 = 9d . . . . simplify
6 = d . . . . . . divide by 9
Substituting into the first equation gives ...
13 = t(1) +2(6)
1 = t(1) . . . . . . . . subtract 12
Using the found values in the equation for the sequence gives ...
t(n) = 1 +6(n -1)
