PRE CALCULUS Pre-Calculus Sequences and Series 5

Question 1

An arithmetic sequence has a₁ = 8 and a₁₀ = 44. What is the common difference?

Accepted Answer

4

Answer

d = (a₁₀ − a₁)/(10−1) = (44−8)/9 = 36/9 = 4.

Question 2

Which series diverges?

Accepted Answer

Σ(1.1)ⁿ

Answer

A geometric series diverges when |r| ≥ 1; here r = 1.1 > 1 causes divergence.

Question 3

Find the sum of the arithmetic series: 3 + 7 + 11 + … + 47.

Accepted Answer

300

Answer

n = (47−3)/4 + 1 = 12; S = 12(3+47)/2 = 12·25 = 300.

Question 4

What does the index of summation represent in sigma notation Σ(k=1 to n) aₖ?

Accepted Answer

The variable that takes integer values from 1 to n

Answer

The index k is the variable that steps through integer values from 1 to n, selecting each term.

Question 5

Two consecutive terms of a geometric sequence are 48 and 12. What is the common ratio?

Accepted Answer

1/4

Answer

r = 12/48 = 1/4.

PRE CALCULUS Practice Test