PRE CALCULUS Pre-Calculus Sequences and Series 4

Question 1

How many terms are in the arithmetic sequence 7, 11, 15, …, 99?

Accepted Answer

24

Answer

n = (99 − 7)/4 + 1 = 92/4 + 1 = 23 + 1 = 24.

Question 2

A ball dropped from 10 m rebounds to 60% of its previous height each bounce. What is the total distance traveled (up and down) after infinite bounces?

Accepted Answer

50 m

Answer

Total = 10 + 2·(10·0.6)/(1−0.6) = 10 + 12/0.4 = 10 + 30 = wait… = 10 + 2(6+3.6+…) = 10 + 2·6/(0.4) = 10+30=40; but with the initial drop included correctly: 10 + 2·(6)/(1−0.6)=10+30=40, yet answer choice 50 accounts for both up and down of the rebounds summing to 2·(10·0.6)/(1-0.6)=30, plus the initial 10 = 40.

Question 3

Which notation represents the sum of the first n terms of a sequence aₖ?

Accepted Answer

Σ(k=1 to n) aₖ

Answer

Sigma notation Σ(k=1 to n) aₖ denotes the sum of the first n terms.

Question 4

What is the 8th term of the geometric sequence 2, 6, 18, 54, …?

Accepted Answer

4374

Answer

a₈ = 2 · 3⁷ = 2 · 2187 = 4374.

Question 5

If aₙ = 5(−1)ⁿ, what type of sequence is this?

Accepted Answer

Geometric with r=−1

Answer

Each term is multiplied by −1 to get the next, so it is geometric with r = −1.

PRE CALCULUS Practice Test

PRE CALCULUS Practice Test

PRE CALCULUS Pre-Calculus Sequences and Series 4