Question

Write an equation for an arithmic sequence such that t(3)=13 and t(12)=67 HELP ASAP

Answer 1

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)