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Express the terms of the following sequence by giving a recursive formula.15 -1, -3, -5 ...О А.Q1= 1/3 and anti(15)an - 15, where n = 1, 2, 3, 4, ...OB.a1ſ and anti = an - 15, where n = 1, 2, 3, 4, ...ОС.Q1and an t1 = an + 16, where n = 1, 2, 3, 4,OD41 = - andanti(1) Jan + 1 g, where n =1, 2, 3, 4, ..

Express the terms of the following sequence by giving a recursive formula15 1 3 5 О АQ1 13 and anti15an 15 where n 1 2 3 4 OBa1ſ and anti an 15 where n 1 2 3 4 class=

Respuesta :

From the sequence:

[tex]\begin{gathered} a_1\text{ = }\frac{1}{3} \\ a_2\text{ = -1}\frac{1}{2} \\ a_3\text{ = -3}\frac{1}{3} \\ a_4\text{ =-5}\frac{1}{6} \end{gathered}[/tex]

If we take the difference between successive session:

[tex]\begin{gathered} a_2-a_1\text{ = }\frac{-11}{6} \\ a_3-a_2\text{ = }\frac{-11}{6} \\ a_4-a_3\text{ = }\frac{-11}{6} \end{gathered}[/tex]

We can thus conclude that:

[tex]\begin{gathered} a_{n+1\text{ }}=a_n\text{ - }\frac{11}{6} \\ a_{n+1\text{ }}=a_n\text{ -1}\frac{5}{6},\text{ where n = 1,2,3,4} \end{gathered}[/tex]

This corresponds to option B

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