- Consider the arithmetic sequence 34252, 34235, 34218,…
Find that last positive term in the sequence.
Since the sequence is decreasing so the formula is
$a_n=-17n+34269$ for finding the nth term
However, I'm not sure how to find the last positive term in the sequence. Should I make $a_n=1$ and solve like this:
$1=-17n+34269$
$-34268=-17n$
$n=2015.76 \approx 2015$
So I would plug in 2015 for n and get 14.
This is how I would think to do it but I'm not sure if I'm correct.
- Consider again the sequence $2018, 1999, 1980, …. $Find the sum of all the positive terms in the sequence.
Again I have $a_n = -19n+2037$
The sum for arithmetic series is $S_n = \frac{n}{2} (a_1+a_n)$
So $a_1 = 2018$
$a_n$ is the last positive term in the sequence so it is
$1 = -19n+2039$
$n = 107.26 \approx 107$
$a_n = 6$
So $S_n = \frac{107}{2} (2018+6) =108284$
- Consider the arithmetic sequence 17, 23, 29, 35, …, 599, 605, whose terms sum to 30789. How many terms are in the sequence?
$30789 = \frac{n}{2} (17+605)$
$n=99$
Best Answer
We need to find a maximal natural $n$ for which $$-17n+34269>0$$ or $$n<2015.82...,$$ which gives $n=2015$ and $$a_{2015}=14.$$
we can solve by the similar way. The answer is true.