Elementary Calculus

Question 1

What is the twenty-first term of the sequence given by xn = 4n - 3 ?

A 6 B 72 C 81 D 87

Question 2

If n is a natural number, what is the sixth term of the sequence given by

xn = 4 × (0.5)n ?

A 0.0625 B 0.125 C 1 D 64

Question 3

What is the fifth term of the sequence {an} = {(1/n)n-1} ?

A 1/5 B 1/25 C 1/125 D 1/625

Question 4

For the sequence defined by an = n2 - 5n + 2, what is the smallest value of n for which an is positive?

A 3 B 4 C 5 D 6

Question 5

The n'th hexagonal number is given by hn = n(2n - 1) What is the sixth hexagonal number?

A 17 B 22 C 66 D 150

Question 6

The nth term of a sequence is given by xn = 3n2 – 1. Which term of the sequence is equal to 866?

A The fifteenth term B The sixteenth term

C The seventeenth term D The twentieth term

Question 7

A The third term B The seventh term

C The eighth term D The tenth term

Question 8

What is the partial sum of the first seven triangular numbers?

A 28 B 56 C 84 D 120

Question 9

What is the partial sum of the squares of the first eight natural numbers?

A 64 B 140 C 204 D 1,296

Question 10

The partial sums of the first n and n + 1 numbers of the Fibonacci sequence are both divisible by 11. What is the smallest value of n for which this is true?

A n = 11 B n = 10 C n = 9 D n = 8