Write an explicit rule

Question

What’s the explicit rule for for this number sequence?

$$\displaystyle{1 \over 100},\ -{3 \over 95},\ {5 \over 90},\ -{7 \over 85},\ {9 \over 80}$$

The numerator changes to negative every other term, while the denominator subtracts $5$ every term.

Do a separate sequence for both and then put it together. You will also need to take the alternating sign in concern too. — randomgirl, Jun 03 '19 at 17:18

beelal · Answer 1 · 2019-06-03T17:44:07.463

3

with convention we start from $n= 0$, $x_n = \frac{(-1)^n(2n+1)}{100-5n}$ for $n=0,1, \ldots, 19$

edited Jun 03 '19 at 17:44

answered Jun 03 '19 at 17:19

beelal

409

1

What happens when $n=20?$ – J. W. Tanner Jun 03 '19 at 17:35
well the sequence isn't defined there, so neither is it's general term – beelal Jun 03 '19 at 17:37

score 0 · Answer 2 · answered Jun 03 '19 at 17:31

The general formula for an (infinite) sequence of (e. g. real) numbers from the finite number $n$ of its (first) members is in principle impossible, as the next (not listed) $(n+1)^\mathrm{th}$ member may be an arbitrary number, and there is still a formula for expressing $a_1, \dots, a_n, a_{n+1}$.

See this answer, in which is for the question

What is the next number of the sequence $1, 2, 3, 4, 5?$

proved by the appropriate formula, that the next number is $\color{red}{1762}.$

Write an explicit rule

2 Answers2