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Quiz

Lesson 1 Quiz: Arithmetic and Geometric Sequences and Series

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1.
The n-th term of an arithmetic sequence with first term a and common difference d is given by:
T_n = a + (n - 1) * d
T_n = a * rn − 1
T_n = a + n * 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:
d = 4 and T_20 = 79
d = 3 and T_20 = 60
d = 5 and T_20 = 98
d = 4 and T_20 = 83
3.
The sum of the first n terms of an arithmetic sequence (S_n) is formulated as:
S_n = n * (a + d)
S_n = a * (1 - rn) / (1 - r)
S_n = n / 2 * [ 2a + (n - 1) * d ] = n / 2 * [ a + l ]
S_n = a / (1 - r)
4.
The common ratio r of the geometric sequence (64, 32, 16, 8, ...) is:
r = 2
r = 4
r = 1/2
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:
r > 1
|r| >= 2
r = 1
|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:
Infinity
24
18
36
7.
If a, b, c form an arithmetic sequence, then the arithmetic mean b equals:
b = sqrt(a * c)
b = 2 a c / (a + c)
b = a + c
b = (a + c) / 2
8.
If a, b, c form a geometric sequence of positive real numbers, the geometric mean b equals:
b = a * c
b = (a + c) / 2
b = + sqrt(a * c)
b = a2 + c2
9.
The sum of the first 10 terms of the geometric sequence 2, 6, 18, 54, ... equals:
118,096
29,524
59,048
19,682
10.
The number of terms in the finite arithmetic sequence (5, 9, 13, ..., 81) is:
19 terms
21 terms
25 terms
20 terms
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