Sequences and Series

Arithmetic Sequence

100

Common difference of 7, 12, 17, 22, …

5

200

Find a₁₀ if a₁=3 and d=4

39

300

Given a₅=26 and d=6, find a₁

2

400

Sum of first 20 terms if a₁=5, d=3

670

500

Which term of 4, 9, 14, … equals 259?

52

Geometric Sequence

100

Common ratio of 3, 12, 48, 192, …

4

200

Find a₆ if a₁=2 and r=3

486

300

Given a₃=27 and r=3, find a₁

3

400

Sum of first 8 terms if a₁=5, r=2

1275

500

Which term of 81, 27, 9, 3, … equals 1/27?

8

Harmonic Sequence

100

Define a harmonic sequence in one sentence.

A sequence whose reciprocals are arithmetic.

200

Is 1, 1/4, 1/7, 1/10, … harmonic? State why

Yes; reciprocals 1,4,7,10,… have d=3

300

Harmonic Sequence with a₁=1/3 and a₂=1/6; find a₃

1/9

400

For a_n = 1/(2 + 5(n−1)), find n when a_n = 1/42

9

500

Two positives have A.M.=8 and H.M.=6; find the numbers

12 and 4

Fibonacci Sequence

100

Next term: 5, 8, 13, 21, __

34

200

Find F₈ given F₁=1, F₂=1

21

300

Find F₁₂ (F₁=1, F₂=1)

144

400

Sum of first 10 Fibonacci numbers (F₁=1)

143

500

gcd(F₃₆, F₂₄)

144