Question

Math Analysis:
Write an explicit formula for the nth term of the sequence.
17. 5, -2, -9, -16
18. 1, 1/3, 1/9, 1/27, 1/81

Answer 1

17. You're adding -7 again and again, so that's the common difference.

\( \color{Black}{\Rightarrow a_n = a_1 + (n - 1) d}\)
Just replace a1 with the first term and d with the difference.

Answer 2

so what's n? o:

Answer 3

so what's n again u only told me a and d D:

Answer 4

n is the number of terms.

Answer 5

so n is 4?

Answer 6

For number 17, yes. However, if you go farther into the sequence, the number changes, so you have to change n for whatever number in the arithmetic sequence.

Answer 7

the answer says its tn=12-7n

Answer 8

You have to use characteristic equations to solve.

Answer 9

since it's a linear recurrence relation

Answer 10

was the equation on top correct?

Answer 11

yea, looks like it, but you have to use characteristic on it for explicit formula.

Answer 12

i dont understand what you mean o-o

Answer 13

someone said n=the number of terms

Answer 14

could you show me how you did the problem

Answer 15

5+(n-1)(-7) = a_n as he said. so 5-7n+7 = a_n so it s a_n = 12-7n.

Answer 16

that's how you get the answer.

Answer 17

if you mean getting to a_n = a_1 + (n-1)d, that's much more complicated to explain,

Answer 18

the steps is:
-writing out a recurrence relation,
-translating it to a explicit formula,

Answer 19

how about #18

Answer 20

what's the answer for #18???
i got 3(1/3)^n