PRE CALCULUS Pre-Calculus Sequences and Series 3

Question 1

In a geometric sequence, a₃ = 12 and a₆ = 96. What is the common ratio?

Accepted Answer

2

Answer

a₆/a₃ = r³ = 96/12 = 8, so r = 2.

Question 2

What is the sum of the first 100 positive integers?

Accepted Answer

5050

Answer

Using Gauss's formula S = n(n+1)/2 = 100(101)/2 = 5050.

Question 3

A sequence is defined by aₙ = n² − n. Which term equals 20?

Accepted Answer

5th

Answer

n² − n = 20 → n(n−1) = 20 → n = 5, so the 5th term equals 20.

Question 4

The sum of a finite arithmetic series with 20 terms is 500. If the first term is 5, what is the last term?

Accepted Answer

45

Answer

S = n(a₁ + aₙ)/2 → 500 = 20(5 + aₙ)/2 → aₙ = 45.

Question 5

Which sequence is neither arithmetic nor geometric?

Accepted Answer

1, 4, 9, 16, …

Answer

1, 4, 9, 16, … are perfect squares; differences grow, so it is neither arithmetic nor geometric.

PRE CALCULUS Practice Test