Recursive sequence nth term (ACT). Game on.

Recursive sequence nth term (ACT) is a grade 9 math skill aligned to Common Core standard HSF.IF.A.3. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 recursive sequence nth term (act) problems our math games drill.

CCSS HSF.IF.A.310 questions in the bank
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Warm-upeasy

A sequence is defined by a1=5a_1 = 5 and an=an1+(n1)a_n = a_{n-1} + (n-1) for n2n \geq 2. The first five terms are 5,6,8,11,155, 6, 8, 11, 15. What is a7a_7?

Continue: a6=15+5=20a_6 = 15 + 5 = 20 and a7=20+6=26a_7 = 20 + 6 = 26.

Mid-gameeasy

A sequence is defined by a1=3a_1 = 3 and an=2an1a_n = 2a_{n-1} for n2n \geq 2. The first four terms are 3,6,12,243, 6, 12, 24. What is a6a_6?

Each term doubles the previous: a5=48a_5 = 48 and a6=96a_6 = 96.

Mid-gameeasy

A sequence is defined by a1=20a_1 = 20 and an=an13a_n = a_{n-1} - 3 for n2n \geq 2. The first four terms are 20,17,14,1120, 17, 14, 11. What is a6a_6?

Subtract 33 each step: a5=8a_5 = 8 and a6=5a_6 = 5.

Mid-gameeasy

A sequence is defined by a1=7a_1 = 7 and an=an1+3a_n = a_{n-1} + 3 for n2n \geq 2. The first five terms are 7,10,13,16,197, 10, 13, 16, 19. What is a6a_6?

Add 33 each step: a6=19+3=22a_6 = 19 + 3 = 22.

Mid-gamemedium

A sequence is defined by a1=4a_1 = 4 and an=an1+2(n1)a_n = a_{n-1} + 2(n-1) for n2n \geq 2. The first five terms are 4,6,10,16,244, 6, 10, 16, 24. What is a6a_6?

Continue: a6=24+2(5)=34a_6 = 24 + 2(5) = 34.

Mid-gamemedium

A sequence is defined by a1=30a_1 = 30 and an=an1(n1)a_n = a_{n-1} - (n-1) for n2n \geq 2. The first four terms are 30,29,27,2430, 29, 27, 24. What is a7a_7?

Continue: a5=20a_5 = 20, a6=15a_6 = 15, and a7=156=9a_7 = 15 - 6 = 9.

Mid-gamemedium

A sequence is defined by a1=1a_1 = 1 and an=an1+n(n1)a_n = a_{n-1} + n(n-1) for n2n \geq 2. The first five terms are 1,3,9,21,411, 3, 9, 21, 41. What is a7a_7?

Continue: a6=41+6(5)=71a_6 = 41 + 6(5) = 71 and a7=71+7(6)=113a_7 = 71 + 7(6) = 113.

Buzzer beatermedium

A sequence is defined by a1=2a_1 = 2 and an=2an11a_n = 2a_{n-1} - 1 for n2n \geq 2. The first four terms are 2,3,5,92, 3, 5, 9. What is a7a_7?

Continue: a5=17a_5 = 17, a6=33a_6 = 33, and a7=2(33)1=65a_7 = 2(33) - 1 = 65.

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