DepEd MELC reviewer for Grade 10 Mathematics, Quarter 1. Study the rules, worked formulas, and exam hacks below.
1
Arithmetic and Geometric Sequences
| Sequence | Pattern | nth term |
|---|---|---|
| Arithmetic | add common difference d | aₙ = a₁ + (n−1)d |
| Geometric | multiply common ratio r | aₙ = a₁ · r^(n−1) |
💡 Exam Hack
Arithmetic = ADD the same number each time. Geometric = MULTIPLY by the same number each time.
2
Series (Sums)
Arithmetic sum: Sₙ = n/2 (a₁ + aₙ)
Geometric sum: Sₙ = a₁(1 − rⁿ)/(1 − r)
Geometric sum: Sₙ = a₁(1 − rⁿ)/(1 − r)
3
Polynomials: Remainder & Factor Theorems
Remainder Theorem: dividing P(x) by (x−r) gives remainder P(r). Factor Theorem: (x−r) is a factor if P(r)=0.
⚠️ Common Mistake
For (x − r), use +r in P(r). For (x + 3), r = −3.
4
Worked Example
Find the 10th term of 3, 7, 11, … (arithmetic, d = 4).
a₁₀ = 3 + (10 − 1)(4) = 3 + 36 = 39
📌 Quick Recap — Master These
Before your test, make sure you can confidently do each of the following:
- Explain and apply Arithmetic and Geometric Sequences.
- Explain and apply Series (Sums).
- Explain and apply Polynomials: Remainder & Factor Theorems.
- Explain and apply Worked Example.
Re-read any section above where you hesitate, then try the worked example again without looking.