Question

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, ..

Answer 1

From the sequence:

`\begin{gathered} a_1\text{ = }(1)/(3) \\ a_2\text{ = -1}(1)/(2) \\ a_3\text{ = -3}(1)/(3) \\ a_4\text{ =-5}(1)/(6) \end{gathered}`

If we take the difference between successive session:

`\begin{gathered} a_2-a_1\text{ = }(-11)/(6) \\ a_3-a_2\text{ = }(-11)/(6) \\ a_4-a_3\text{ = }(-11)/(6) \end{gathered}`

We can thus conclude that:

`\begin{gathered} a_{n+1\text{ }}=a_n\text{ - }(11)/(6) \\ a_{n+1\text{ }}=a_n\text{ -1}(5)/(6),\text{ where n = 1,2,3,4} \end{gathered}`

This corresponds to option B