Precalculus Sequences and Series Quiz: 10 Questions with Explanations

A \(3\)B \(\frac12\)C \(-4\)D \(-3\)

Each term is 3 less than the previous term, so d = -3.

A 54B 59,049C 39,366D 20

a_10 = 2 times 3^9 = 2 times 19,683 = 39,366. Using 3^10 gives the next term.

A \(a_{n}=4n+1\)B \(a_{n}=5n+4\)C \(a_{n}=4n+5\)D \(a_{n}=5\cdot4^{n-1}\)

d = 4 and a_1 = 5, so a_n = 5 + 4(n – 1) = 4n + 1.

A -15B 13C -24D -13

a_12 = 9 + 11(-2) = -13. Using 12 instead of n – 1 = 11 gives -15.

A 2B 3C 4D 1/2

Each term is twice the previous term: 6/3 = 12/6 = 2.

A 50B 55C 45D 100

S = 10/2 (1 + 10) = 55.

A \(1+\frac12+\frac14+\text{ … }\)B \(1+2+4+\text{ … }\)C \(1+1+1+\text{ … }\)D \(3+4.5+6.75+\text{ … }\)

Only a series with |r| < 1 converges; here r = 1/2.

A 2B 1C \(\frac12\)D It has no sum

a_1 = 1/2 and r = 1/2, so S = (1/2)/(1/2) = 1, as the bar shows.

A It is arithmetic with difference 2B It is geometric with ratio 2C It is geometric with ratio 3D It is not a sequence

Multiplying the previous term by 2 each time makes it geometric with r = 2.

A 15B 8C 16D 32

S = 8/(1 – 1/2) = 16. The partial sums approach 16.