Sequences

Finding the rule behind a list of numbers — linear on both tiers, quadratic and geometric on Extended — and using it to answer questions listing cannot.

หลักสูตรแกนกลาง / สสวท.: จำนวนและพีชคณิต (Number and Algebra)ตรงกับ ม.5 ลำดับและอนุกรม (ส่วนลำดับ)
Common Core (US): F-BF, F-LE
Cambridge: IGCSE 0580 — Topic 2: Algebra and graphs (Core and Extended)

4.1 Linear sequences

Finding the $n$ th term

1Find the common difference $d$
2Start from $d n$
3Compare with the sequence and add or subtract the gap
4Test on the first term and on a later one

ตัวอย่าง

Find the $n$ th term of $7, 11, 15, 19, \dots$ and decide whether $103$ is in the sequence.

วิธีทำ

1. $d = 4$ , so start with $4 n$ : $4, 8, 12, 16$
2.The sequence is $3$ more: rule is $4 n + 3$
3.Set $4 n + 3 = 103$ , so $n = 25$ — a whole number

ตอบ $4 n + 3$ ; yes, $103$ is the $25$ th term

ทำไมถึงเป็นแบบนั้น

That second half is what the rule is FOR. Asking whether a number appears becomes a one-line equation, and a non-integer answer settles it — no listing required.

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