Sequences and series. Game on.

Sequences and series is a grade 11 math skill aligned to Common Core standard HSF.BF.A.2: write arithmetic and geometric sequences both recursively and with an explicit formula, and use them to model situations. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 33 sequences and series problems our math games drill.

CCSS HSF.BF.A.233 questions in the bank
Kickoff

8 plays. No signup.

Warm-upeasy

In an arithmetic sequence, the fifth term is 2020 and the sixth term is 14.14\textsf{.} What is the ninth term?

The common difference is 14−20=−6.14 - 20 = -6\textsf{.} From the sixth term to the ninth term there are 33 steps, so the ninth term is 14+(−6)×3=−4.14 + (-6) \times 3 = -4\textsf{.}

Mid-gameeasy

Find the 55th term: a1=3a_1 = 3, d=4d = 4.

a5=3+4(4)=3+16=19a_5 = 3 + 4(4) = 3 + 16 = 19.

Mid-gameeasy

Find the sum: 1+2+41 + 2 + 4.

Geometric series with a1=1a_1 = 1, r=2r = 2, n=3n = 3. Sum =1+2+4=7= 1 + 2 + 4 = 7.

Mid-gameeasy

In a geometric sequence, the second term is 66 and the third term is 18.18\textsf{.} What is the sixth term?

The common ratio is 186=3.\dfrac{18}{6} = 3\textsf{.} From the third term to the sixth term there are 33 steps, so the sixth term is 18×33=486.18 \times 3^{3} = 486\textsf{.}

Mid-gameeasy

Find the 44th term: a1=2a_1 = 2, d=5d = 5.

a4=2+3(5)=2+15=17a_4 = 2 + 3(5) = 2 + 15 = 17.

Mid-gameeasy

Find the sum: 3+6+123 + 6 + 12.

Geometric series with a1=3a_1 = 3, r=2r = 2, n=3n = 3. Sum =3+6+12=21= 3 + 6 + 12 = 21.

Mid-gameeasy

In a geometric sequence, the third term is 88 and the fourth term is 16.16\textsf{.} What is the seventh term?

The common ratio is 168=2.\dfrac{16}{8} = 2\textsf{.} From the fourth term to the seventh term there are 33 steps, so the seventh term is 16×23=128.16 \times 2^{3} = 128\textsf{.}

Buzzer beatereasy

Find the 44th term: a1=5a_1 = 5, d=3d = 3.

a4=5+3(3)=14a_{4} = 5 + 3(3) = 14.

Overtime

25 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

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