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17 multiple-choice questions and 10 flashcards on Sequences and Series, about 11% of the High School Algebra 2 bank. Every one carries a written rationale.
Sequences and Series is one of 9 chapters in CoStudy's High School Algebra 2 bank, and it holds 17 of the bank's 150 multiple-choice questions — roughly 11% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
10 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
Evaluate: ln(e³).
Answer: C — 3 (ln(eˣ) = x, so ln(e³) = 3)
ln = natural log (base e). ln(eˣ) = x. ln(e³) = 3. Inverse function property. ln(1) = 0, ln(e) = 1. Algebra 2 logarithm foundations.
Solve: 2log(x) = log(36).
Answer: D — x = 6 (rewrite: log(x²) = log(36); thus x² = 36, x = 6 (positive solution; logs require x > 0))
Use power property: 2log(x) = log(x²). So log(x²) = log(36) → x² = 36. x = ±6. But log requires x>0, so x=6 only. Check domain in log equations.
What is the discriminant of x² - 4x + 4 = 0?
Answer: A — 0 (b²-4ac = 16-16 = 0; one repeated real root)
Discriminant b²-4ac. Here 16 - 16 = 0. Zero discriminant: one repeated real root. Positive: two distinct real roots. Negative: two complex conjugate roots. Indicates nature of solutions.
Find the 12th term of an arithmetic sequence with a₁ = −2 and d = 5.
Answer: A — 53
a₁₂ = a₁ + (n − 1)d = −2 + 11·5 = 53. B) Used n instead of n−1. C) Sign error on a₁. D) Used 10 instead of 11.
What is the SUM of an arithmetic series with first term 5, last term 25, and 6 terms?
Answer: E — 90 (sum = n(a₁+aₙ)/2 = 6(5+25)/2 = 6·15 = 90)
Arithmetic series sum: S_n = n(a₁ + a_n)/2 = 6(5+25)/2 = 6 · 15 = 90. Foundation for series problems. Algebra 2 sequences and series.
Which transformation does y = f(x) + 3 represent?
Answer: C — Shift UP 3 (adding constant outside function shifts vertically up)
Function transformations: y = f(x) + c shifts up c units. y = f(x) - c shifts down. y = f(x - c) shifts right c (inside function!). y = f(x + c) shifts left. Common Algebra 2 transformation rules.
Which is the conjugate of 3 + 2i?
Answer: E — 3 - 2i (complex conjugate negates imaginary part)
Complex conjugate of a + bi is a - bi. Conjugate of 3 + 2i is 3 - 2i. Used in dividing complex numbers: multiply by conjugate to rationalize. Important Algebra 2 concept.
What is the SUM of the roots of 2x² - 7x + 3 = 0? (use Vieta's formulas)
Answer: A — 7/2 (sum of roots = -b/a = -(-7)/2 = 7/2)
Vieta's formulas for ax²+bx+c=0: sum of roots = -b/a, product = c/a. Here sum = -(-7)/2 = 7/2; product = 3/2. Useful shortcut. Verify by solving: roots are 3 and 1/2; sum = 7/2 ✓.
Find the 15th term of an arithmetic sequence with a₁ = 3 and common difference d = 4.
Answer: D — 59
A) Computed (n − 1)d = 14 × 4 = 56 but forgot to add a₁. B) Used n × d = 15 × 4 = 60 instead of (n − 1)d. C) Used a₁ + n·d = 3 + 15(4) = 63. D) a_n = a₁ + (n − 1)d = 3 + 14(4) = 3 + 56 = 59.
Sum of first 6 terms of 1 + 2 + 4 + 8 + …:
Answer: A — 63
Geometric, r = 2. S₆ = 1(1 − 2⁶)/(1 − 2) = (1 − 64)/(−1) = 63. B) Off by one — confused with a₇. C) Sum of 7 terms. D) Just the 6th term.
4 cards from the 10 in this chapter.
How can you solve a 2-variable system?
Substitution, elimination, or graphing.
What's an 'arithmetic sequence'?
Each term is obtained by adding a constant (common difference) to the previous.
What's the sum of the first n terms of an arithmetic sequence?
Sₙ = n(a₁ + aₙ)/2.
Find the 10th term of: 5, 8, 11, 14, ...
32. (a₁ = 5, d = 3; aₙ = 5 + 9(3) = 32.)
These are a sample. The full Sequences and Series chapter runs 27 items with per-chapter progress tracking, on the web and in the iOS app.
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