Interactive Quiz and Assessment: Lesson 1 - Arithmetic and Geometric Sequences and Series

1

The n-th term of an arithmetic sequence with first term a and common difference d is given by:

A T_n = a + (n - 1) * d B T_n = a * r^(n - 1) C T_n = a + n * d D T_n = 1/2 n (2a + d)

2

In the arithmetic sequence (3, 7, 11, 15, ...), the common difference d and the 20th term (T_20) are respectively:

A d = 4 and T_20 = 79 B d = 3 and T_20 = 60 C d = 5 and T_20 = 98 D d = 4 and T_20 = 83

3

The sum of the first n terms of an arithmetic sequence (S_n) is formulated as:

A S_n = n * (a + d) B S_n = a * (1 - r^n) / (1 - r) C S_n = n / 2 * [ 2a + (n - 1) * d ] = n / 2 * [ a + l ] D S_n = a / (1 - r)

4

The common ratio r of the geometric sequence (64, 32, 16, 8, ...) is:

A r = 2 B r = 4 C r = 1/2 D r = -1/2

5

The sum to infinity (S_infinity) of a geometric series exists and converges if and only if the common ratio satisfies:

A r > 1 B |r| >= 2 C r = 1 D |r| < 1 (i.e. -1 < r < 1), and S_infinity = a / (1 - r)

6

The sum to infinity of the geometric series 12 + 6 + 3 + 1.5 + ... equals:

A Infinity B 24 C 18 D 36

7

If a, b, c form an arithmetic sequence, then the arithmetic mean b equals:

A b = sqrt(a * c) B b = 2 a c / (a + c) C b = a + c D b = (a + c) / 2

8

If a, b, c form a geometric sequence of positive real numbers, the geometric mean b equals:

A b = a * c B b = (a + c) / 2 C b = + sqrt(a * c) D b = a^2 + c^2

9

The sum of the first 10 terms of the geometric sequence 2, 6, 18, 54, ... equals:

A 118,096 B 29,524 C 59,048 D 19,682

10

The number of terms in the finite arithmetic sequence (5, 9, 13, ..., 81) is:

A 19 terms B 21 terms C 25 terms D 20 terms