The Life Starter
Sign up
Grade 11 · unit review

Review: Algebra2: Sequences, Sums, and Recursion

A sequence distinguishes an indexed term from the sum of several terms. Arithmetic and geometric structures support different formulas, while a recursive definition determines each next term from previously defined values.

Download reviews and answer keys

Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. An arithmetic sequence has a₁=7, common difference 3. Find a_8.
Need a hint?
  • An arithmetic sequence adds the same common difference between consecutive terms.
  • The number of steps is one less than the term position.
2. Find the sum of the first three terms of a geometric sequence starting at 7 with ratio 2.
Need a hint?
  • A geometric sum adds several values whose consecutive ratio is fixed.
  • A geometric term formula alone does not give a sum.
3. Find the sum of the four-term arithmetic sequence 7,9,11,13.
Need a hint?
  • Terms equally far from opposite ends of an arithmetic sequence have equal pair sums.
  • Use the stated number of terms, including both endpoints.
4. A recursive sequence has a₁=7 and a_(n+1)=3a_n+1. Find a₂.
Need a hint?
  • A recursive definition names a starting term and an operation producing the next term.
  • The subscript labels a position rather than multiplication.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. An arithmetic sequence has a₁=9, common difference 3. Find a_10. Candidate answers: (A) 35 (B) 36 (C) 37 (D) 72. 2. Find the sum of the first three terms of a geometric sequence starting at 9 with ratio 2. Candidate answers: (A) 126 (B) 62 (C) 63 (D) 64. 3. Find the sum of the four-term arithmetic sequence 9,11,13,15. Candidate answers: (A) 47 (B) 48 (C) 49 (D) 96. 4. A recursive sequence has a₁=9 and a_(n+1)=3a_n+1. Find a₂. Candidate answers: (A) 27 (B) 28 (C) 29 (D) 56.

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. 36. Term 10 is 9 steps after term 1. Therefore a_10=9+3(9)=36. The exponent rule for geometric sequences is not used. 2. 63. The three terms are 9,18,36. Their sum is 63. Using a(1−r³)/(1−r) gives the same result when r=2. 3. 48. Pair first with last and second with third; each pair sums to 24. Two pairs total 48. Equivalently S=4(first+last)/2. 4. 28. Apply the supplied rule once to a₁: a₂=3(9)+1=28. The subscript n marks a term position, not a multiplication by n.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.