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2 years ago

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

Mathematics

1 answer:

ale4655 [162]2 years ago

7 0

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)

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)

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