Question

Given the following sequence of numbers find the recursive formula, and the appropriate sequence formula,(arithmetic or geometric) and find the next three numbers in the sequence.8. 3, 9, 15, 21, 27,9. 5, 9, 13, 17, 21,10. -243, 81, -27, 9,11. Using the sequence find the n for the following terms 6, 1, 4,-9...... -254

Answer 1

see explanation below

Step-by-step explanation:

8) 3, 9, 15, 21, 27

The common difference = 15-9 = 9-3

The common difference = d = 6

Hence, it is an arithmetric sequence

The recursive formula:

`\begin{gathered} a_(n+1)=a_n+\text{ 6} \\ \text{OR} \\ a_n=a_(n-1)+\text{ d} \\ a_n=a_(n-1)+6 \end{gathered}`

The appropriate formula:

`\begin{gathered} a_n=a_1+\text{ (n-1)d} \\ \text{where a}_1\text{ = }3\text{ } \\ a_n=3_{}+\text{ (n-1)d} \end{gathered}`

The next three numbers in the sequence:

`\begin{gathered} \text{The last term in the sequence given was 6th term. } \\ \text{The next }3\text{ terms will be: 7th, 8th and 9th term} \end{gathered}`
`\begin{gathered} a_7\text{ = 3 + (7-1)}*6 \\ =\text{ 3+ (6)(6) = 3 + 36} \\ 7th\text{ term = }a_7=39 \end{gathered}`
`\begin{gathered} a_8\text{ = 3 + (8-1)}*6 \\ =\text{ 3+ (7)(6) = 3 + 4}2 \\ 8th\text{ term = }a_8\text{ =}45 \end{gathered}`
`\begin{gathered} a_9\text{ = 3 + (9-1)}*6 \\ a_9\text{ = }3\text{ + 8(6) = 3 + 48} \\ 9th\text{ term = }51 \\ \end{gathered}`