Trixie wants to create an especially tricky arithmetic sequence. she wants the 5th term of the sequence to equal 11 and the 50th term to equal 371. that is, she wants t(5) = 11 and t(50) = 371. is it possible to create an arithmetic sequence to fit her information? if it is possible, find the rule, the initial value t(0), and the common difference for the arithmetic sequence. if it is not possible, explain why not.

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jimrgrant1 jimrgrant1 · Answer 1 · 2018-09-22T12:18:03+02:00

-21, - 13, - 5, 3, 5, ....

using the nth term formula for an arithmetic sequence

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d

we require to find [tex]a_{1}[/tex] and d

[tex]a_{5}[/tex] = [tex]a_{1}[/tex] + 4d → (1)

[tex]a_{50}[/tex] = [tex]a_{1}[/tex] + 49d → (2)

subtract equation (1) from equation (2)

45d = 360 ⇒ d = [tex]\frac{360}{45}[/tex] = 8

substitute d = 8 into equation (1)

[tex]a_{1}[/tex] + 32 = 11

[tex]a_{1}[/tex] = 11 - 32 = - 21

- 21, - 13, - 5, 3, 11 are the first 5 terms of the required sequence.